The graves outside the shrine are packed tightly together, thick stripes of cement with small concrete blocks poking out of the earth at either end. Some of the graves are about six feet apart, like those marking the remains of Khalid Abushahma, the first protester to be shot dead by Muammar Gaddafi's forces in this Libyan port city on 20 February, and of Ali al-Hadi, who died just two days ago.

Other graves barely span two feet. Ibrahim Omran, a baby buried on 7 April. Amina Abdullah, a small girl, two weeks before. Sanad Aduraat, a toddler killed by a bullet on 6 March. Carved into the cement next to Aduraat's name, next to all the names, is the word al-shaheed, meaning martyr.

"Gaddafi is the reason for all this," said Abdullah Almohandis, an old man in a brown hooded cloak who oversees the cemetery.

Heavy explosions boomed in the distance, as they do here for many hours of each day and night. Almohandis held his open hands to the sky, shaking with rage.

The war in Misrata is now two months old. The graveyards are filling up and the hospitals are overflowing. In their attempt to end the uprising, Gaddafi's forces have killed at least 1,000 people. Around 90% are civilians who have died because of indiscriminate shelling or shooting, doctors here say.

Fighting has been so heavy that parts of the city centre are now almost completely destroyed. Buildings, homes and mosques are pockmarked with bullet holes. Walls have been completely blown away, or are blackened by fire. Entire suburbs near the front lines are empty of families, who have crammed into other parts of the city, closer to the sea. Communications have been completely cut. Burnt-out cars and tanks litter the streets, alongside effigies of the dictator who has ruled Libya for 42 years.

The resistance from the rebels – from all the people in Misrata – seems remarkable given their limited armoury and experience. That they have managed to keep Gaddafi's forces to one side of the city seems a miracle, or at least a masterclass in guerrilla warfare. But this is a siege, and while the rebels can defend their lines, they do not have the means to fight their way out, or to send their families to safety. And despite significant losses, Gaddafi remains determined to fight his way in.

The cost is huge. Besides the dead, more than 3,000 people in this city have been injured since the conflict began. Many have been hit by shrapnel from indiscriminate shelling by Gaddafi's forces. Others have been picked off by snipers, including Mohamed Hassan, 10, who was hit in the head when he opened his front door last Saturday. He now lies in Misrata's hospital, screaming for his father and uncle or jabbering incomprehensibly. His mother, Zeinab, touches his forehead. Her tears have run dry. She tries to speak but then shakes her head and looks down.

Nobody here in Libya's third largest city expected a war. A few dozen people went out to protest on 17 February, in sympathy with people in Benghazi, where the main uprising began. Police arrested the protesters, sparking bigger demonstrations. Then security forces opened fire. About 70 people were killed in a matter of days. The city rose up in anger.

"We kicked out all of Gaddafi's people, who fled to Tripoli," said Mohamed Karwad, a 23-year-old graphic designer, who was one of the first protesters to be arrested. "At that time we had nothing but rocks and Molotov cocktails." When Gaddafi's forces returned two weeks later it was with tanks and armoured vehicles. The rebels still had few proper weapons, but they had taken measures to prevent the city from falling. They blocked the main streets with shipping containers full of sand and metal, preventing the tanks from passing though. They laid down blankets soaked in diesel that became caught in the tanks' tracks. A Molotov cocktail heaved from a sidestreet would then set the tank alight. Mosques played recordings of "God is Great" over and over to inspire the rebel fighters, infuriating Gaddafi's forces. Many mosques have since been hit by shells.

Fighting was fierce and bloody. Many rebels died, but so did many of Gaddafi's men, and each time the rebels took their weapons. Some were welded on the backs of pickups, which were then reinforced with giant steel plates on the front and back. Despite repeated attempts, the tanks have been unable to penetrate the city centre. But by sending snipers into abandoned buildings Gaddafi's forces have managed to stop the rebels taking ground quickly. It's a slow and deadly fight, street by street.

The rebels appear to have no central leadership, but are divided into cells around the neatly laid-out city, commanded by men with noms de guerre such as Lion of the Desert, or Big Deer. Roadblocks appear every few hundred metres, some made of giant mounds of sea-sand, others of concrete pipes or ladders or chairs.

Many of the fighters manning them – the Shabab, as they are known – are young. Mohamed Mustafa, 19, was studying first-year medicine when the revolution began and missing his parents, who are living in Nottingham, where his father is pursuing a PhD. He was clutching an AK-47, with a checked scarf wrapped around his head. Every day he spends six hours at the checkpoint near Benghazi Street, a scene of fierce fighting in recent weeks, searching cars and passengers for unauthorised weapons or satellite phones. "At the start I saw how people were dying for the cause of freedom," he said. "So I decided to join the troops and defend my people and my home from the devil that is Gaddafi."

Across Benghazi Street, close to the vegetable market now used as a base by Gaddafi's forces, the rebels have punched holes in the walls of some houses to create new roads that offer more protection from sniper fire. There were few signs of life, apart from a few unfortunate chickens, until we reached a house whose garage was filled with fighters.

"Revolutionaries having breakfast," shouted one of them, holding up a bread roll filled with tuna.

Aiman al-Hadad, a 25-year-old engineer, clutched a sniper's rifle that had been captured from Gaddafi's forces. Growing up, he had shot birds, he said, so it was natural to become a sharpshooter when the war began. He had killed seven of Gaddafi's men, he said proudly.

Mohamed Elfituri, a young pharmacist, was more modest, saying that they were making gains, but that Gaddafi's snipers remained a threat. His fiancee was in Tripoli, he said, and he had not been able to reach her for two months. Might it be possible to send an email on his behalf?

Their commander had been killed the previous day, so Mohamed Shinisheh was now in charge. Solidly built, and the only one of his men wearing a beret and uniform, he had been working in Malta as a builder before the uprising. He rushed to Benghazi, the rebel headquarters in the east, received three weeks' training and took a boat to Misrata.

"In the day, in the night, we fight," he said. "We are defending our positions. Gadaffi's troops are just 50 metres away."

He moved up the road with a few of his men, running quickly across open patches of road, and pointing out where the snipers had hit water tanks and electricity lines to make life more difficult for the rebels. At a corner a tattered green flag erected by Gaddafi's troops during a brief occupation hung above a house that had since been taken by the rebels. A shop was on fire, hit by an incoming shell an hour before.

A short drive away, close to Tripoli Street, which Gaddafi's forces have been trying to capture since the battle began, Mohamed Swesi, 42, who fought in Chad for the Libyan army in the 1980s, was showing off an IED he had made using two landmines, a dozen bullets and an ammunition case. Three members of his family had been killed by Gaddafi's army. He was not afraid to die. "My heart is big," he said. "Give me good weapons and I'll be in Tripoli in three days."

Dozens of young fighters sat quietly on the side street, each clutching a weapon. They were waiting for Gaddafi's snipers, who they say are now cut off from the rest of their forces, to show themselves in the pockmarked buildings that line Tripoli Street. Many of the marksmen had been killed but a significant number remained. In front of one house was pool of fresh blood. A 12-year-old boy from a family that had refused to leave their home had been hit as he stepped outside to play. He died immediately.

An ambulance passed. The doctor, Mohamed Bashir, said they had already picked up three dead people that morning. More than 20 had been injured. "We will stay here and fight Gaddafi until the last blood spills."

Blood is spilling too from those who do not want to fight – women, children and elderly people – thanks to the indiscriminate shelling by Gaddafi's forces. In the private clinic that now serves as Misrata's main hospital, Mokhtar Naria, 37, and his 10-year-old nephew, Mortaz, both had bandages around their heads.

The Narias had left their home to cram in with four other families in an area that was meant to be safer. But earlier this week, as they were preparing to pray, a shell burst through the roof. Six people were injured, including Naria's grandfather, who lost a finger. Naria had a damaged skull. He could walk, but seemed dazed. "The boy does not even know about Gaddafi," said his father. "He just knows he is afraid."

Upstairs, Dr Fathi Mohamed was doing his rounds in the surgery ward. Before the revolution began, he had seen two gunshot wounds in six years. Now he has seen hundreds, and many more shrapnel injuries. He sent 36 wounded people by boat to Benghazi on Wednesday night, but still has 19 people in his ward alone.

"The oldest we have treated was 92 years old. He had chest injuries but did not die. The youngest was one year old."

An ambulance arrived. It was carrying a rebel fighter – a man who until eight weeks ago had been a civilian deeply fearful of Gaddafi and who had now been killed by government forces. Tomorrow the name Osama Manita will be written in concrete somewhere in Misrata, perhaps near the shrine. One more martyr.