The two men appeared at a party cabinet meeting for the first time since the quarrel began, and then Mr Howard says they spoke privately for about half an hour.
Mr Howard told reporters after the meeting, that during their discussion Mr Costello did not specially ask him to stand aside immediately or before Christmas.
Mr Howard says he does not believe their professional relationship has broken down and as far as he’s concerned its business as usual.
“It is the overwhelming desire of the parliamentary Liberal Party … that Mr Costello and I in our current positions continue to work for the benefit of the Australian people and for the benefit of the Liberal Party,” he told a packed press conference this afternoon.
Mr Howard said that obviously Mr Costello would like to see a favourable leadership change before the next election, but he declined to comment when asked if he would run for election again saying only “I haven’t called the news conference to talk about my medium- to long-term future.”
Mr Howard said he harboured no resentment towards Mr Costello for his leadership ambitions, “There is no personal venom that’s ever been part of our relationship.”
He admits that the public quarrel may hurt his party in the short term, “We’ve had bad days before. I think the public makes a judgment over a longer period than two days.”
Mr Howard said he was confident his working relationship with Mr Costello would be restored. “We have been a very strong team. We’ve, obviously, had a bad few days.
Mr Howard also refused to comment when asked if Mr Costello’s recent behaviour had hurt his chances of becoming party leader, but did say he still believed that if he was to fall under a bus, Mr Costello was the person most likely to succeed him as prime minister.
Adding quickly, “I am still very careful about crossing the road.”
Mr Howard again insisted there was no leadership deal with Mr Costello.
A smiling Mr Costello emerged from the federal cabinet meeting in Sydney refusing to say anything more about the leadership to the pack of reporters waiting outside.
Mr Costello had little more to say when he touched down at Melbourne Airport.
A confident treasurer was met by a small posse of waiting journalists, but did not reveal the contents of the conversation he had with Mr Howard.
“I had a full-on press conference this morning, I answered all the questions that the press had and what I said was entirely accurate about what has happened in relation to these matters,” he said.
Mr Costello also dodged questions about his future.