The prime minister, Malcolm Turnbull, has praised the Muslim community as "respected and valued" in Australian society, in a speech community leaders have said will go some way towards mending fences with the government after strained relations with Turnbull's predecessor, Tony Abbott.

"I want to emphasise to each and every one of you that the Australian Muslim community is respected and valued," he said in a speech to the Islamic Council of Victoria on Monday. "And we do not consider or talk about or contemplate the Muslim community solely through the prism of security.

"You are an integral part of an Australian family that's bound together by the shared values of freedom, democracy and the rule of law."

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