Tunis (AFP) - Tunisia is hunting a third suspect in the massacre of tourists at its national museum, President Beji Caid Essebsi said, after admitting security failures at the Bardo.

"Definitely there were three," Essebsi told France media iTele television and Europe 1 radio.

"Two were killed, but there is one who is now on the run," he said. "In any case, he will not get very far."

Wednesday's attack on the National Bardo Museum in Tunis killed 20 foreign tourists and a policeman, and was the first assault claimed by the Islamic State group in the North African country.

It came as Tunisia -- the birthplace of the Arab Spring that held its first free elections last year -- struggles with rising Islamist extremism.

On Saturday, authorities released CCTV footage showing two black-clad gunmen with automatic weapons walking unimpeded though a large lobby in the Bardo, just after noon.

The grainy footage then shows the gunmen passing an unidentified male. They point an automatic weapon at him briefly before letting him leave as they make their way up a staircase.

After rampaging through the museum for several hours, the two gunmen were killed in an assault by security forces.

Secretary of State for Security Rafik Chelly said Sunday on the website of French weekly Paris Match the third person in the video was "one of the two Vespa drivers that brought the killers", and that he wanted to leave because of the police response.

"The drivers and other logistics people from the cell, a total of 15 people, are already behind bars," Chelly added. The interior ministry had earlier said more than 10 people were arrested.

- Guards having coffee -

The interior ministry said on Saturday it had issued an arrest warrant for Maher Ben Moudli Kaidi, a Tunisian suspect described as a "dangerous terrorist element".

According to Chelly, Kaidi coordinated the attack.

Officials have admitted that guards tasked with protecting the museum and the nearby parliament were having coffee at the time of the assault.

Essebsi acknowledged that more could have been done to prevent the attack, which raised fears for the lucrative tourism sector that represents eight percent of Tunisia's gross domestic product (GDP).

Museum curator Moncef Ben Moussa told AFP on Sunday the Bardo would reopen on Tuesday and that all of its the artefacts were "intact".

Essebsi admitted "there were failures" in the country's security mechanism, in an interview with Paris Match.

"The police and intelligence were not systematic enough to ensure the safety of the museum," he said.

But he also insisted his security forces were quick to respond after the attack and to prevent further deaths.

"We were there 10 minutes later," he told iTele and Europe 1.

Essebsi also vowed that an anti-terrorism law "will be voted rapidly", adding: "Libya is one of our problems."

Officials said the Bardo gunmen had trained in neighbouring Libya, where IS has militant camps and is battling local militia for control of the country's oil wealth.

Both Tunisia and Libya have seen an upsurge in Islamist extremism since separate uprisings that toppled veteran strongmen in 2011.

- IS threat -

But Tunisia has taken pride in forming a democratic government -- in marked contrast to Libya or Egypt, which has also been shaken by turmoil since its 2011 revolt.

The IS group has threatened more attacks in Tunisia.

The dead tourists were four Italians, three Japanese, three French, two Spaniards, a Colombian, an Australian-Colombian, a British woman, a Belgian woman, three Poles and a Russian.

On Sunday, Essebsi laid a wreath at the museum for the victims, who included a Tunisian policeman.

The attack in the heart of Tunis was unprecedented, but dozens of police and military personnel have been killed in attacks blamed on Islamist militants, who are battling the army in the Mount Chaambi region near the Algerian border.

A Tunisian soldier was killed and two others injured when their vehicle hit a landmine "planted by terrorist elements" in a mountainous region near the Algerian border, the defence ministry said.

Tunisian newspapers demanded that the authorities do more to combat extremism.

"What's essential now is to really take action," French-language daily Le Quotidien wrote, including more controls at mosques "under the influence of uncontrollable religious fanatics".

Le Temps called for "urgent draconian measures" and withdrawing Tunisian citizenship from "terrorists who pledge allegiance to the enemy".

Authorities say as many as 3,000 Tunisians have gone to Iraq, Syria and Libya to join IS and other jihadist groups, raising fears of returning battle-hardened militants plotting attacks.

Essebsi said there are "sleeper cells" that must be identified.