A mosque has been vandalised while two others are inviting Australians to see Islam for themselves following Australia’s biggest anti-terrorism operation.

Australia’s Muslim leaders are distancing their community from those stung in the recent anti-terror raids but the actions of a few are challenging efforts.

In a bid to dispel fears about Islam, two mosques in southeast Queensland, in the same region where anti-terrorism raids were carried out on Thursday, have opened their doors to the public.

The move accompanies a reassurance from the Grand Mufti of Australia, Dr Ibrahim Abu Mohammad, and leaders of a number of Muslim community organisations that Australians have nothing to fear from their Muslim neighbours.

“We have a vested interest in the safety and security of Australia,” Dr Mohammad said.

The leaders noted a dramatic increase of abuse and discrimination against Muslim Australians in recent weeks, and revealed a special Facebook page had been set up in response.

Police fears about retribution to the operation that targeted an alleged terror plot came to fruition with the vandalism of a mosque in Queensland.

Vandals spray painted the word “Evil” across a mosque at Mareeba, near Cairns, drawing strong condemnation and disgust from local mayor Tom Gilmore.

“The thing that is deeply saddening is that it has been in this community since the mid-fifties,” he told AAP.

Hours after hundreds of police rolled out the pre-dawn raids across Sydney suburbs on Thursday morning, detaining 15 people, protesters criticised the police action.

Hundreds gathered at the demonstration in Lakemba, in Sydney’s west, on Thursday night claiming the raids were unjustified and used the Muslim community as a scapegoat.

The rally action attracted a stern warning from Prime Minister Tony Abbott.

He said he would be very disappointed in Australians supporting anything that could lead to executions.

“Anything of that nature is utterly reprehensible,” he said.

“That’s why I would say to those people who were noisily demonstrating – that very small group that was noisily demonstrating in Lakemba last night – have a good, long, hard look at yourselves.”

Out of those arrested in the raids Omarjan Azari, 22, is facing the most serious allegation – preparing a terrorist plan involving what police allege was “random selection” of members of the public for execution.

He is accused of conspiring with one of the Islamic State’s senior Australian figures, Mohammad Baryalei.