By Hadeel Al Shalchi

CAIRO, Sept 29 (Reuters) - Egypt's army-backed authorities have extended the detention of two Canadians held without charge since political clashes in mid-August as officials investigate a small remote control aeroplane and other items found in the pair's hotel room.

The Canadian government called earlier this month for Tarek Loubani, a doctor, and John Greyson, a filmmaker, to be released.

The two men, who have been on hunger strike for 13 days, face a range of charges including arson, murder, and attacking a police station which come with the allegation they participated in illegal demonstrations by supporters of deposed President Mohamed Mursi in the city on Aug. 16.

They have been held along with hundreds of other detainees in what they say are squalid conditions in Cairo's Tora prison since and say they were on their way to Gaza to work and had gone only to observe the protests during a layover in Cairo.

A foreign ministry spokesman said officials had found surveillance equipment including a camera attached to a small plane during a search of their hotel room and would hold the men while investigations continued.

"We cannot jump to conclusions about spying charges, the prosecution needs to finish investigations. Now, they are being charged with participation in illegal demonstrations," spokesman Badr Abdelatty told Reuters.

"We were told that there was a drone in the hotel room, that is usually used to attach a camera on it. I don't know if there was already a camera on the drone when they found it."

The men's lawyer, Marwa Farouk, said they deny all charges against them.

According to a statement on the website http://tarekandjohn.com/ the pair were in Cairo en route to the Gaza Strip where Loubani was due to teach a medical course while Greyson made a documentary about him.

During the layover in Cairo, they went to observe the protests and were arrested that evening at a check point when they stopped to ask for directions after buying ice cream.

They were searched and beaten before being taken to Tora, where leading members of Mursi's Brotherhood are also being held.

"The Canadians were searched and arrested while they were out after the curfew," Abdelatty said.

"In their hotel room, a search found a USB stick containing film of the burning Fath mosque and of armed protesters, sophisticated communication equipment, and a small plane that can hold a camera that takes footage from the air."

The pair describe prison conditions including sleeping on concrete floors with cockroaches, sharing a cell with three dozen other men, and not being allowed phone calls.

Farouk said it was possible their detention could be extended again in November.

Egypt's prosecutor general discussed the case with the Canadian ambassador in a meeting last Thursday.

"They met for one hour where the prosecutor explained to the ambassador the case and the evidence available," Abdelatty said. "He also emphasized the importance of respecting Egypt's sovereign judicial process and avoiding foreign interference."

At least 2,000 people, most of them Mursi supporters, have been arrested since the army ousted him on July 3 in response to mass protests against his rule.

The security forces killed hundreds of Mursi supporters on Aug. 14, when police and army moved to break up two Cairo protest camps set off after his downfall. Amnesty International says scores of those arrested since have been deprived of their basic legal rights. (Reporting by Hadeel Al-Shalchi; Editing by Tom Perry and Patrick Graham)