Greens Leader Senator Christine Milne has called on the Abbott government to deny an extremist alleged to have masterminded anti-Muslim violence in Sri Lanka entry to Australia.

Gnanasara Thero, who has been instrumental in inciting hatred against religious minorities in Sri Lanka and who is the General Secretary of the extremist Bodu Bala Sena sect, has applied for a visa and intends to tour Australia. Gnanasara Thero has reportedly been denied entry to the UK, France and the US.

The Australian Greens are rejecting praise from a visiting member of the Rajapaksa family, saying it was not a "bold move" to withhold support from a UN war crimes investigation, but rather a shameful demonstration that Australia is appeasing the government in Sri Lanka to further Tony Abbott's domestic policies on asylum seekers.

The Australian Greens say Tony Abbott's cruel refugee policy and Operation Sovereign Borders condemns Australia to a deteriorated relationship with Indonesia.

"This is Tony Abbott in action. He is an embarrassment internationally and at home," Greens Leader Christine Milne said.