Another policeman was seriously injured in the attack at the Gisozi museum, where concrete tombs house the remains of some 250,000 Rwandans killed in and around the capital Kigali.

"A man walked to the museum and threw a grenade at the policemen on guard. It killed one of them instantly," police spokesman Marcel Higiro said. "It must be one of those extremist fellows still harbouring the genocide ideology."

Rwanda is in the fifth day of an official week of mourning that follows the 14th anniversary of the start of 100 days in which Hutu extremists slaughtered 800,000 ethnic Tutsis and moderate Hutus.

Some Hutus complain that the mourning period, in which all bars and other recreational facilities are closed and flags are flown at half mast, enforces a perception of collective guilt against their majority ethnic group.

The attack came as a surprise in a country with a low crime rate and police were still hunting the culprit.

Police take a tough approach under President Paul Kagame, who has said it is necessary to stop potential revenge attacks in a nation where many know and live near the killers of their families.

Kagame is a Tutsi, and led the rebel army that overthrew the Hutu-led government which helped orchestrate the genocide.

His policy of zero tolerance for divisive ethnic speech has won both praise for healing Rwanda, and criticism by some who view it as a sign of autocratic tendencies.

The Gisozi genocide museum is a regular stopover for visiting dignitaries, and recently hosted U.S. President George W. Bush.