* Could hit debates, rallies ahead of elections - activists

* Thousands in streets as new law announced

* Future demonstrations will need police permission (Adds more details, comment from rights activist)

By Maggie Fick

CAIRO, Nov 24 (Reuters) - Egypt's president signed a new bill into law on Sunday restricting rallies and other public gatherings, a move likely to raise fresh questions about the army-backed government's democratic credentials.

Thousands of anti-government protesters were on the streets of Cairo and other cities when the new bill was announced on state media, as they have been regularly in the nearly three years since autocrat Hosni Mubarak was ousted.

The new legislation will require them to get advance permission from the police before gathering in the future, according to a draft seen by Reuters.

"This is quite dangerous ahead of elections - in normal times also, but (particularly) ahead of elections," said Ziad Abdel Tawab of the Cairo Institute for Human Rights, adding it could disrupt public meetings including debates and rallies.

President Adli Mansour's approval of the law came as a 50-member committee prepared to vote on an amended constitution that will be put to a referendum expected in coming months. Parliamentary and presidential elections are due next year.

Rights groups had urged Mansour to reject the draft presented to him by the cabinet installed after the army overthrew Mubarak's successor, Islamist President Mohamed Mursi, in July.

"The draft law seeks to criminalise all forms of peaceful assembly, including demonstrations and public meetings, and gives the state free hand to disperse peaceful gatherings by use of force," read a joint statement issued on Friday by 19 Egyptian organisations.

Thousands of supporters of Mursi and his Muslim Brotherhood demonstrated in Cairo and in several other cities, marking 100 days since security forces crushed two pro-Mursi sit-ins in Cairo, killing hundreds.

Police fired teargas to disperse some of the demonstrations on Sunday.

There was no immediate sign of any reaction to the new legislation on the streets.

The Brotherhood has faced a harsh security crackdown since Mursi's ouster. Thousands have been arrested and its senior leaders jailed. (Editing by Michael Georgy)