CAIRO, Nov 19 (Reuters) - Protesters scuffled with Cairo police on Monday during a rally by 5,000 people to mark the first anniversary of the death of at least 42 Egyptian demonstrators during interim military rule.

The demonstration underscored public pressure on elected Islamist President Mohamed Mursi to punish killings and abuses during security crackdowns by the military council that replaced Hosni Mubarak after his fall in a popular revolt last year.

The issue of holding leaders of the Supreme Council of the Armed Forces (SCAF) to account touches a sensitive nerve since the generals intended to ensure immunity from prosecution before they ceded power, diplomats say.

In November 2011, police pulled down the tents of protesters who had camped in Tahrir Square overnight after a demonstration of some 50,000 people, mostly Islamists, against the SCAF.

That prompted thousands of protesters to return to the square and clashes erupted. Police beat protesters with batons and fired rubber bullets and tear gas at them. Protesters broke off chunks of cement from sidewalks to throw back at the police.

The clashes, in which at least 42 protesters died, have since been coined "Mohamed Mahmoud events" after the street in which they took place.

In Monday's demonstration, stones and empty bottles were hurled and 24 people were injured, including four policemen.

"We swear by your blood martyrs, there will be another revolution!" demonstrators chanted on Monday, waving Egypt's flag and posters of people who died during the clashes.

"Down, down with rule by the guide!" they added, suggesting Muslim Brotherhood leader Mohamed Badie pulls the strings even though Mursi officially quit the Brotherhood on taking office.

The demonstrators were mostly youth from the non-Islamist camp, including Ultras soccer fans, Revolutionary Socialists, and public figures such as leftist activist Kamal Khalil.

Mahmoud Street, where they gathered, is located off Tahrir Square, the epicentre of the mass demonstrations that forced out Mubarak, and also near the interior ministry.

During SCAF rule, at least 12,000 civilians were tried by army courts and over 100 protesters were killed in clashes with army and police, with thousands more injured, rights groups say.

"We want justice for the martyrs and purging of the corrupt interior ministry, and we want Mursi to adopt a public plan for reform of the police forces and the country in general," said Nader Eissa, one of the demonstrators on Monday. (Reporting by Saad Hussein; Writing by Shaimaa Fayed; Editing by Mark Heinrich)