Mosques and Islamic centres across Australia are holding a national day of sermons to denounce an Islamic State fatwa against Australians.

Mosques across Australia are condemning terrorist acts carried out in the name of Islam.

The Australian National Imams Council is holding a national day of sermons, a day after a man was charged with spraying menacing graffiti on a mosque at Rocklea, in Brisbane’s south.

More than 250 mosques and Islamic centres are taking part in a “national khutbah day” to condemn murderous atrocities committed by jihadist groups such as Islamic State.

“The sermons will denounce the recent so-called fatwa from overseas targeting Australia and reiterate that it has no religious authority and is unequivocally rejected,” the council said in a statement.

“The sermons will reiterate that the horrors conducted overseas in the name of religion are crimes against humanity and sins against God.

“That the violence being perpetrated against innocent people is not sanctioned in Islam, by the prophets or the Koran.”

Prime Minister Tony Abbott has declined to say if he believed religious tensions had heightened when asked about the defacing of the Brisbane mosque.

“What I’m concerned is about increased crime, particularly terrorist crime,” he told the Seven Network on Friday.

“I’m very concerned about that and the assurance I want to give to the Australian public is, first and foremost, your government will do everything we humanly can to keep you safe.”

On Thursday night, a 34-year-old man was charged with spraying graffiti on the Rocklea mosque.

He is due to face Brisbane Magistrates Court on October 22 on charges of wilful damage, trespass, public nuisance and possessing a graffiti instrument.

Brisbane Lord Mayor Graham Quirk condemned the vigilante action, with the alleged graffiti crime occurring a week after the word “Evil” was scrawled across a mosque at Mareeba, in far north Queensland.