Australia's prime minister says the Australian ambassador has returned to Jakarta in a sign that the anger and tense relations that followed Indonesia's execution of two Australian drug traffickers had eased.

Paul Grigson in April became the first Australian ambassador to be recalled from Indonesia as a protest after Australians Andrew Chan and Myuran Sukumaran were among eight drug convicts executed by Indonesian firing squads.

Prime Minister Tony Abbott said Wednesday that Grigson returned on Monday after a five-week absence because he had been gone for an appropriate time.

Abbott told reporters his government wasn't going to let the executions "permanently damage what is a very good friendship and a very important relationship."