He reiterated that their talks were focused on the Pacific region.
Asked about a request for New Zealand to take children in detention from Nauru, Peters said Prime Minister Jacinda Ardern had not approached Nauru, saying it was a request from an NGO, and the matter was one between Nauru and Australia.
Bishop said the Pacific Islands Forum was an opportunity for those nations to put a topic on the table.
Australia and New Zealand did not dictate the subject of the talks.
Peters said no one country could be singled out when asked about China's influence in the Pacific.
Bishop tried to end the press conference but Peters lingered to answer one more question, saying he would look like a chauvinist if he didn't answer a question from the reporter, a woman.
As he was leaving the stage, Peters gave a word of advice - if you're going to have a leadership spill, take an abacus.