It is "essential" the Muslim community is fully involved in the next stage of tackling terrorism in the UK, MPs say.
MPs said Muslims felt they were being stigmatised
Relations between ethnic communities have worsened since 11 September 2001, the Home Affairs Select Committee said.
Asians were not being targeted by police, but there was a "clear perception" among Muslims they were being stigmatised, its report said.
It followed a five-month inquiry into how the terrorism threat was affecting community relations.
The MPs also said religious leaders should condemn followers who advocated violence, particularly those "organising and propagating extremist ideas sympathetic to terrorism".
"They must be identified and dealt with effectively - not only by the authorities, but most importantly by the Muslim community itself," the report said.
The committee also said more should be done to tackle Islamophobia and anti-Semitism.
Muslim leaders should continue to condemn "forcefully and unequivocally" attacks on Jews by members of their community, said the MPs.
The Board of Deputies of British Jews supported this view, blaming "the export of anti-Semitic views from Arab states in the Middle East" for attacks against Jews.
Michael Whine, the board's director of defence, said Muslims needed to "make sure that tension doesn't overspill from the Middle East to the streets of Britain".
The Muslim Council of Britain said it would condemn attacks on people regardless of their background.
But Iqbal Sacranie, secretary general of the council, added "genuine and proper criticism" of Israel's policies is not anti-Semitic and must not be silenced.
The MPs said they did not believe the Asian community was "being unreasonably targeted" by the police in their application of the Terrorism Act or using stop-and-search powers.
A large majority of stop-and-searches in England and Wales took place in London, where the proportion of Asians targeted was "very close" to their proportion in the overall population, the report found.
However, "special efforts" should be taken by the police and government to reassure Asians they were not being unfairly singled out, said the MPs.
But Mr Sacranie is unhappy at their conclusion, calling for monitoring of police stop-and-searches in terms of religion rather than race.
He said Muslims "cannot be simply identified on the race factor," because they were part of the white, black and Asian communities.
The MPs called for research into why a "very small number of young Britons" turn to extremist groups.
While admitting community relations had deteriorated since 2001, committee chairman John Denham said there were "many positive initiatives" showing the way forward.
"Leadership is the key to dealing with the issues arising from terrorism and community relations," he said.
"Local leaders, faith leaders and central government all have their parts to play in building cohesive communities."