"I will be resigning from my cabinet position as Minister for Foreign Affairs", Bishop said in a statement, signaling her intention to remain on the backbench.
Last week Ms Price called for the Liberal party to adopt rules making it more hard for the party room to spill sitting Prime Ministers.
The possibility that Ms Bishop could leave Parliament before the next election will be a major concern for Mr Morrison, Mr Turnbull's former treasurer, because it opens the possibility of another by-election being held for her seat.
Morrison, who was sworn Australia's Prime Minister on 24 August, chose to roll the cyber security functions into the Department of Home Affairs instead of appoint a replacement to Angus Taylor who resigned on 23 August. In Malcolm Turnbull's cabinet, Fletcher was the Urban Infrastructure Minister.
Dumping Malcolm Turnbull has smashed the Liberal vote, catapulting Bill Shorten ahead as the country's clear preferred prime minister, according to a new poll.
India rejects UAE govt's $100 million flood disaster fund offer
But it was graceful enough to take help even from many poor countries which were usually at the receiving end of American aid. Before this, India used to accept aid from the worldwide community in the wake of a big natural calamity.
Now, one Western Australian MP has told the West Australian they felt tricked into voting against Bishop in an apparent bid to keep Dutton out. He said Angus Taylor, a Dutton supporter, would be the new energy minister. Every single man and woman in the Liberal Party room needs to put that type of behaviour behind us and make sure we do unify for the future.
A trailblazer who was Australia's first female foreign minister and the Liberals' first female deputy leader, the 62-year-old was hailed by her peers Sunday.
Danielle Blain, a key Bishop ally and fundraiser for the WA Liberals, said Ms Bishop would be remembered as one of the most significant ministers to come from this State.
Former deputy prime minister Barnaby Joyce, who resigned from cabinet in February, will become special envoy for drought assistance and recovery.
Mr Turnbull is yet to announce his resignation from the seat but told reporters last week it would be "not before too long". "She has set the bar for the next Foreign Minister very high".