He stressed that his coalition had decided to keep binding MPs on same-sex marriage on Tuesday, but Mr Abbott also said that the party had not "finalised a position to take to the next election".
He said: "I think I can say arising out of today that if you support the existing definition of marriage between a man and a woman, the Coalition is absolutely on your side but if you would like to see change at some time in the future, the Coalition is prepared to make that potentially possible.
"But the disposition, as I said, is that it should happen through a people's vote rather than simply through a Parliament's vote."
According to the Sydney Morning Herald the press conference came after a five and half-hour party room meeting called to deal with the issue of same-sex marriage.
The move angered some members, and several senior ministers criticised the way the debate was conducted.
Mr Abbott also commented that backbenchers could vote with their consciences if they so wished: "I'm not saying the Coalition's position is set in stone for all time."
Coalition MP, Warren Entsch, who was one of the first to raise the issue of same-sex marriage, said he was disappointed but not angry with the outcome.
In a statement he said: "In the party room today, during the six hours of discussion, there was potential for highly emotive, over the top debate," he said in a statement.
"However I have to commend my colleagues for the robust and respectful standard of the conversation, notwithstanding the fact that there were diametrically opposed views."
He also confirmed he would still introduce a cross-party bill to legalise same-sex marriage next week but suggested it could now fail without a free vote for coalition MPs.
