Mr Taylor on Wednesday resigned from the Liberal front bench, where he had served as opposition defence spokesman, saying Ms Ley was unfit to lead the Liberals going forward.
Party conventions require anyone who wants to challenge their leader to step down from a portfolio.
The resignation comes before an expected leadership spill, although Mr Taylor did not say whether he had requested a ballot or a party room meeting.
The resignation allows Mr Taylor to openly canvass for votes before a likely ballot.
He said the party had lost its way under Ms Ley's leadership.
"The Liberal Party is at the worst position it has been since 1944, when the party was formed," he told reporters in Canberra.
"That is a confronting reality and we cannot ignore it. We have failed to hold a bad Labor government to account.
"I don't believe Sussan Ley is in a position to be able to lead the party, as it needs to be led from here.
"What we need right now is strong leadership, clear direction and a courageous focus on our values."
Mr Taylor said the delay in tendering his resignation on Wednesday was due to Ms Ley holding a meeting with Israeli president Isaac Herzog, who was in Canberra for talks as part of a state visit.
"The process here more generally, for all of us, has been to talk about the future of our party as Liberals. We want to see a strong Liberal Party, and we know that means we need strong leadership," he said.
Supporters claim Mr Taylor has the numbers to defeat Ms Ley in a vote, but the result is anticipated to be tight.
Mr Taylor said he would consult with colleagues about the direction of the party.
"I am absolutely committed to restoring confidence in the Liberal Party, to ensure that Australians regain confidence in the Liberal Party and steering the Liberal Party back to where it needs to be," he said.
Moderate MP Tim Wilson said he continued to back Ms Ley's leadership of the Liberal Party.
"I have said consistently that I expect leadership, and I expect leadership to drive a vision for the future of the country. I expect leadership to define who we are as a political movement," he told ABC's 7.30 program.
"I've seen her consistently show a steely resolve despite National Party separations, terrorist attacks, an unrelenting assault by Anthony Albanese and his bully boys on the front bench who have tried at every point to knock her about."
Mr Taylor had not spoken with him about asking for his vote in a ballot, he said.
Ms Ley and Mr Taylor contested the Liberal leadership in May after the coalition suffered its worst defeat at a federal election.
Ms Ley narrowly won that vote 29 to 25, but three of her supporters have since left the party room, with numbers expected to be tight.
She has led the party for nine months and is the first female leader of the Liberal Party and first female opposition leader.
Queensland MP Andrew Wallace backed Ms Ley to continue as opposition leader.
"We need to give Sussan Ley time. I think, unfortunately, people have been trying to undermine Sussan from day one," he told Sky News on Wednesday night.
"We shouldn't be knifing the first Liberal woman leader that we have had in under 12 months."
Liberal senator Jacinta Nampijinpa Price said she would support Mr Taylor as leader.
"If we do not make this change, we will be wiped out at the next federal election. We are in a dire situation," she told Sky News.
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