Australia's prime minister has brushed off controversy over his office's treatment of the gay partner of the Australian ambassador to France.

Fairfax Media reported on Wednesday that Ambassador Stephen Brady offered to resign after a disagreement involving Prime Minister Tony Abbott's reception in Paris last month.

It reported Abbott's travelling party sent an instruction that Brady's partner Peter Stephens should not take part in greeting Abbott on the tarmac and should wait in a car.

Brady ignored the instruction and Stephens remained to welcome Abbott as he arrived from Turkey. Australia's Department of Foreign Affairs and Trade later rejected Brady's resignation.

Abbott told reporters he didn't know at the time that his office had told Stephens to wait in a car. He says he doesn't concern himself with "trivia."