According to the Nine News, the lower house is due to resume its work on September 10.
Prime Minister Turnbull agreed to hold another party's meeting on Friday provided he received an official petition signed by the majority of Liberals. He also pledged to resign if the Liberal Party's lawmakers requested a vote for a new leader during Friday's meeting.
Later in the day Australian Foreign Minister Julie Bishop announced that she would run for the post of leader of the Liberal Party, according to Sky News Australia.
READ MORE: Australian Prime Minister Sets Conditions for Resignation
On Tuesday, Turnbull barely managed to defend his Liberals' leadership in a vote initiated by Dutton. However, earlier on Thursday, several more senior members of the government, including Finance Minister Mathias Cormann, said they had lost confidence in the country's prime minister.