Martin Sellner,leader of the right-wing Identitarian Movement of Austria.Credit:Alamy
"Most donations were in the area of two-to-three figures,whereas this donation was in the low four-figure area,"Bacher said."This made it stand out,and the events in New Zealand put a face to this donation."
He said the investigation against Sellner is based on Austrian anti-terror laws.
"We need to determine whether there is a connection and if so,whether it's criminally significant,"said Bacher.
Sellner denied having anything to do with the March 15 massacre,in which 50 Muslims were killed in the southern New Zealand city.
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Australian 28-year-old Brenton Tarrant was arrested within an hour of the mosque shootings and has been charged with murder.
"I had nothing to do with the attack,"Sellner said in a video statement posted on YouTube,adding that he would donate the money to a charitable organisation.
He suggested the reason for the donation might have been to provoke repressive measures against"patriots".
The ABC reported last week that Tarrant also made a donation to Australian far-right group United Patriots Front.
Austrian authorities said last week that the Christchurch shooter visited Austria,but declined to confirm when or whether he met with any far-right activists during his trip.
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Some of Tarrant's anti-Muslim views are echoed by the Identitarian Movement. The group is close to sections of the nationalist Freedom Party,which is part of the country's coalition government.
Austria's vice chancellor,who leads the Freedom Party,echoed Kurz's call for a comprehensive probe into possible Austrian ties to the Christchurch gunman.
"All suspicions of extremism are acted upon,whether they are right,left or religiously motivated,"Heinz-Christian Strache said on Twitter."Fanaticism has no place in our society."