The back-room bloodletting that has come to typify Australia’s turbulent politics claimed one conservative prime minister and anointed another on Friday, in the sixth change to the country’s leadership in 11 years.

By the time the new prime minister, Scott Morrison, formerly the country’s treasurer, emerged from the room where Liberal Party lawmakers elected him on Friday, his colleagues had ousted his predecessor, shut down the lower house of Parliament and blown up their own signature piece of energy legislation — all in the span of a week.

Members of the governing party forced out Prime Minister Malcolm Turnbull — the fourth time an Australian leader has been undone by his own party since 2010 — leading many citizens to complain that the country’s officials were more interested in “Game of Thrones”-style political machinations than actual governance.

Mr. Morrison, 50, an erstwhile ally of Mr. Turnbull, was a compromise candidate who initially distanced himself from those who led the insurgency. In his first news conference after the vote, Mr. Morrison pledged to end the infighting and “heal the party.”