The boat, carrying 88 passengers and two crew, was spotted by a border patrol aircraft northwest of Darwin on Sunday.
A Customs vessel went to assist the boat and those on board are being transferred to Christmas Island for assessment.
It is the first boat to be intercepted by Australian authorities since the coalition’s election victory on Saturday.
Mr Abbott has promised instant action to deter asylum seekers.
‘We will make a difference from day one. I believe we can stop the boats in a term of government,’ he has said repeatedly, including during his election campaign.
Mr Abbott said a coalition government will put in place processes to turn back boats when it is safe to do so.
‘These are Indonesian crewed, Indonesian flagged, Indonesian home-ported vessels that have a right to access Indonesia,’ Mr Abbott has said.
Indonesia has rejected the coalition plan to turn back boats, sparking concerns that relations between the two countries could turn rocky.
But Mr Abbott said the Howard government successfully turned back boats without compromising the regional relationship.
AAP has sought comment from the incoming government on the latest boat arrival.