A bitterly divided Tory leadership is thought to have forced former London Mayor Boris Johnson from the contest.
In a news conference where he was expected to launch his campaign to succeed David Cameron as Tory leader - and Prime Minister - Johnson said, "I have concluded that person cannot be me."
Johnson, who led the campaign to get the UK out of the EU, did not name who he believes should be Tory leader.
Johnson's shock decision to rule himself out of the Conservative election race comes after justice Secretary and fellow Brexit campaigner Michael Gove's surprise announcement on Thursday morning that he would run for leader.
Home Secretary Theresa May is also among the candidates. Nominations shut at noon.
BBC assistant political editor Norman Smith said it was an "astonishing turn of events".
He said that Gove's decision to contest the Conservative party leadership had led to Boris Johnson's decision not to take part.
House of Commons leader Chris Grayling, who is backing May as Conservative leader, says the contest now features a "number of skilled, effective performers."
The 59-year-old May is now the bookies' favourite to win the contest. She has held the Home Office brief since 2010, and is a former Tory party Chair.
As well as Gove and May, the line-up of Conservative candidates vying to be party leader and Prime Minister are: Liam Fox, Stephen Crabb and Andrea Leadsom.
The remarkable turn of events on Thursday come with the Labour party itself in turmoil after mass resignations from leader Jeremy Corbyn's shadow cabinet.
Earlier on Thursday, senior Labour figure Angela Eagle said she will challenge Corbyn for the Labour leadership.
It is understood the former shadow business secretary has the support of the 51 MPs needed to mount a challenge.
Eagle is one of 20 members of the shadow cabinet to have quit since Sunday, after which MPs approved a motion of no confidence in Corbyn.