Jeremy Hunt and Nadhim Zahawi have been eliminated from the first round of the Tory leadership race.
Former Chancellor of the Exchequer Rishi Sunak topped the poll with the most support from his colleagues in the hotly contested race.
The former health secretary and current Chancellor received the least number of votes from the over 350 Conservative MPs during the race to replace Boris Johnson as Prime Minister.
READ MORE: Penny Mordaunt favourite among Tory members to be next Prime Minister, poll finds
Candidates needed the backing for 30 Conservative MPs to get to the next round of the contest which is due to take place on Thursday.
Sunak, Liz Truss, Penny Mordaunt, Kemi Badenoch, Tom Tugendhat and Suella Braverman remain in the running to replace Boris Johnson as Prime Minister.
The final two candidates chosen by Tory MPs will spend the summer battling it out to win the support of Conservative members, with their choice of the next prime minister being unveiled on September 5.
Johnson would formally tender his resignation to the Queen the following day to make way for his successor, his official spokesman confirmed.
It comes as Boris Johnson's press secretary insisted the PM is "staying neutral" despite his remaining loyalists throwing their support behind Liz Truss.
Sunak, who currently commands the most public declaration of support from Tory MPs, faced claims from the Foreign Secretary's supporters of implementing "economically damaging" policies.
They have also attacked his campaign with claims it has engaged in "dirty tricks" to manipulate the Tory leadership race that will select the next prime minister.
Asked if No 10 is involved in a "stop Sunak" operation as the first round of voting loomed on Wednesday, Johnson's press secretary said: "No."
She declined to say whether Downing Street remains supportive of the former chancellor, whose resignation helped end Johnson's grip on No 10.
The press secretary said she did not know whether Mr Johnson discussed backing Truss with Nadine Dorries and Jacob Rees-Mogg before they made their public declaration in Downing Street.
"He's staying neutral in this contest," the spokeswoman said.
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