The opposition Labor Party has seized on the issue, noting that it recently pledged to make same-sex marriage legal within 100 days if returned to power in the next elections. Last month, a former Labor prime minister, Julia Gillard, came out in support of same-sex marriage, drawing scorn from some who noted that she had opposed it while in office.

Mr. Abbott, a Jesuit-educated Catholic who spent three years studying for the priesthood, has called same-sex marriage a “very deeply personal” issue and one “on which decent people can differ.” He has proposed that Australian voters decide the issue directly, in a referendum or a nonbinding plebiscite. He has been vague about how such a vote would be conducted, but he said that it would probably be held after the next elections.

“I’m just saying that if there is to be change, it should be change that’s owned by the people, not just by the Parliament,” Mr. Abbott said in a radio interview.

Critics have called that an attempt to dodge the issue, and Liberals and others have assailed him for preventing lawmakers in the party from voting as they see fit on the bill.

Some Liberals were unhappy that Mr. Abbott included lawmakers from their smaller, more conservative coalition partner, the Nationals, in the Aug. 11 meeting, which they say skewed the result. (Even within the Nationals, there is dissent: A youth division of the party endorsed same-sex marriage last week.)

Mr. Abbott noted that opposition to same-sex marriage was in the coalition’s platform when it won the 2013 elections. Allowing lawmakers to contradict that, he said, would have left supporters feeling cheated (or “dudded,” as Australians say). “The last thing you should do is dud the people who voted for you,” he said.

For her part, Ms. Forster sees same-sex marriage as entirely consistent with the party’s conservative values. She called it “deeply disappointing” that Liberals were not allowed to vote their conscience on the issue.