His top lieutenants in shadow cabinet James Paterson and Jonno Duniam are the latest to tender their resignations on Thursday morning.
Mr Taylor resigned from the shadow cabinet as the opposition defence spokesman on Wednesday night, telling leader Sussan Ley he no longer supported her leadership, but he stopped short of confirming a challenge.
In a five-minute press conference that followed, he didn't call for a spill or articulate any separate policy platform or direction if he were to become leader.
He announced his intention to challenge in a social media post on Thursday morning, while his colleagues Phil Thompson and Jess Collins delivered a letter to Ms Ley asking for an urgent party room meeting to resolve the leadership.
"I'm running to be the leader of the Liberal Party because I believe that Australia is worth fighting for," he said in a minute-long video.
"I believe we need strong and decisive leadership that gives Australians clarity, courage and confidence in providing a vision for the future.
"I'm committing myself to the cause of restoring our party so that it can be the party that Australians expect and deserve."
Mr Thompson and conservatives Matt O'Sullivan and Claire Chandler were the first to tender to follow Mr Taylor in resigning from the shadow ministry announcing they would back the leadership change.
Senator O'Sullivan said the coalition "lacks the policy clarity, leadership and strategic direction required to rebuild trust with voters and present a compelling alternative government".
Ms Ley has responded in her own post, saying she would take the pressure off families, fix the budget and keep Australians safe.
Mr Thompson said a leadership change was needed to turn the party's dire electoral fortunes around, as it hits hits lowest polling on record.
"We have been in a death spiral, and we need to get out of it. Angus Taylor has the ability to do that," Mr Thompson told reporters in Canberra.
The vote is likely to be held on Thursday night or Friday morning, with timing complicated because Liberal senators are tied up in parliamentary hearings on Thursday.
Ms Ley is weighing up the pros and cons of calling the meeting immediately and waiting an extra day, balancing the need to strip Mr Taylor of momentum against letting him, and deputy leader aspirant Jane Hume, face scrutiny over past failings during the election campaign.
Ms Ley's backers concede any leadership vote will be tight, while Mr Taylor's camp insist they have the numbers.
Supporters of the current opposition leader argue she hasn't been given enough time to improve the party's position.
Backbench senator Sarah Henderson, who has been at daggers drawn with Ms Ley since the election after she was dumped from shadow cabinet, declared her support for Mr Taylor and backed Senator Hume to run as his deputy.
"We cannot continue as we are. We've declined very rapidly since the election," Senator Henderson told reporters in the corridors of parliament.
Shadow attorney-general Andrew Wallace and housing spokesman Andrew Bragg said they still backed Ms Ley.
