CAIRO (AFP) - Egypt's Muslim Brotherhood called a wave of rallies on Friday in support of ousted president Mohamed Mursi as the military appealed for conciliation despite a crackdown on Islamist leaders.

Ahead of the rallies, around a dozen low-flying military jets screeched across Cairo, a day after they staged a parade leaving a trail of smoke in the shape of a heart in the sky.

The call for "peaceful protests" across Egypt came from the Brotherhood's recently-formed National Alliance to Support Legitimacy, which it said were "to denounce the military coup against legitimacy and in support of the legitimacy of President Mursi".

With thousands of Mursi supporters camped outside a Cairo mosque encircled by military vehicles, the call for demonstrations raised fears of fresh violence after days of bloodshed.

The military said it supported the right to peaceful protest, but warned against violence and acts of civil disobedience such as blocking roads.

Human Rights Watch called for "prompt, impartial investigations to determine who was responsible for killings" since late June.

"The available information indicates that both supporters and opponents of Mursi - and possibly security forces as well - were responsible for needless loss of life," said HRW's Joe Stork.

In the Sinai, Islamist militants killed a soldier early on Friday, as gunmen ambushed army and police positions with machineguns and rockets.

State news agency MENA said military Apache helicopters struck a militant's vehicle in pursuit of gunmen who attacked an airport in the north of the restive peninsula.

Some militants in the Sinai had threatened a violent response after Mr Mursi's ouster on Wednesday.

Clashes also broke out in the Nile Delta province of Sharqiya, hours after chief justice Adly Mansour, 67, was sworn in on Thursday as interim president until new elections.

The army warned Egyptians against resorting to "exceptional and autocratic measures against any political group".

"The armed forces believe that the forgiving nature and manners of the Egyptian people, and the eternal values of Islam, do not allow us to turn to revenge and gloating," added the army, even as security forces rounded up top Muslim Brotherhood officials.

The Islamists accuse the military of conducting a brazen coup against Mr Mursi, Egypt's first democratically elected but controversial president, following massive protests calling for his ouster.