Germany, France, Japan still in the run.
Swedish defense firm Saab, France's state-controlled naval contractor DCNS and Germany's ThyssenKrupp Marine Systems have expressed interest in the project.
However, but Abbott ruled Sweden out over its lack of recent experience.
"The last Australian submarine came off the production line in about 2001. As I understand it the last Swedish submarine came off the production line in about 1996, so it's almost two decades since Sweden built a submarine," Abbott told reporters.
"We are working with the three countries that have continuous, relevant submarine experience."
Sources have said Australia is strongly considering buying a version of the 4,000-tonne Soryu-class submarine built by Japan's Mitsubishi Heavy Industries and Kawasaki Heavy Industries to replace its ageing Collins-class fleet.
Abbott had promised something closer to an open tender process in an attempt to shore up support ahead of a challenge to his leadership from within the ruling Liberal Party last week. He survived but emerged weakened from the internal revolt.
He had pledged ahead of his election in 2013 that up to 12 submarines would be built at state-owned shipbuilder ASC in South Australia state, before beginning to back-pedal last year by signaling that cost and timely delivery were paramount.
That placed the embattled Abbott under enormous political pressure at home, where powerful labor unions and the political opposition have demanded a domestic build to boost Australia's languishing manufacturing industry.
His government had ruled out an open tender in December, appearing to put Japan in the box seat before the recent change of course around the leadership challenge.
For Japan, such a deal would mark its re-entry into the global arms market after Prime Minister Shinzo Abe ended a ban on weapons exports last year.
Japanese sources with knowledge of the deal have told Reuters that if Australia issued a formal tender, political sensitivities meant it was highly unlikely Japan would take part.
The project had long been expected to cost around A$40 billion, but Abbott on Friday revised that figure upwards to A$50 billion, making it by far the most expensive defense procurement project in Australia's history.