SYDNEY, Australia — Malcolm Turnbull, Australia’s prime minister, survived a challenge to his leadership Tuesday, narrowly fending off a more conservative rival after growing speculation that he had lost the support of his party.

Mr. Turnbull called for a vote among Liberal Party colleagues in the wake of a failed effort to win support for an energy bill that would aim to reduce both prices and climate emissions. He won the vote over Peter Dutton, the Home Affairs minister, 48 to 35, and later called for a return to business as usual.

“When we’re united we can continue to deliver great results,” he said. Smiling and aiming to look calm at a news conference in Canberra, he added: “It’s really important that we put differences behind us and get on with our job of looking after the 25 million Australians who put us here.”

But the victory for Mr. Turnbull may be fleeting. Mr. Dutton, who resigned from his post as Home Affairs minister immediately after the loss, will move to the backbench, where he is expected to rally support for another challenge as early as Thursday.