Andrea Leadsom and Michael Gove are battling it out to join Home Secretary Theresa May on the ballot to become the next Conservative leader and PM.
The Brexit-backing rivals came second and third behind the home secretary after the first round of voting whittled the field down to three.
Liam Fox and Stephen Crabb withdrew and gave Mrs May – who wanted a vote to Remain in the EU – their backing.
Mrs Leadsom and Mr Gove both say the next PM must have campaigned for Leave.
One of Mrs Leadsom’s supporters, Defence Minister Penny Mordaunt, claimed there was a “concerted effort” being made to cast doubt on her “stellar career” in the City before becoming an MP.
The Leadsom campaign responded to a report in The Times – which claimed her career had been exaggerated – by publishing a summary of her CV setting out her various banking roles.
Mrs May got 165 of 329 votes cast by Tory MPs on Tuesday. Mrs Leadsom came second with 66 and Mr Gove got 48.
Given the margin of Mrs May’s lead, she is almost certain to feature on the two-person ballot to be put to Conservative members.
The eventual outcome is due on 9 September.
Speaking on BBC Radio 4’s Today programme, Mrs Mordaunt dismissed the suggestion some of Mrs May’s supports could back Mr Gove in the next round of voting in an effort to prevent Mrs Leadsom’s name being on the final shortlist of two presented to members.
“I would say to all my colleagues on Thursday, if you are voting for a candidate who you do not think is the best person to lead this country, you are doing something wrong.”
Mr Gove’s supporters insist he can be trusted despite his dramatic 11th hour decision to turn on ally Boris Johnson and launch his own campaign.
Culture Minister Ed Vaizey told Today the U-turn had “caused Michael some difficulty” but said colleagues would “trust a man who was prepared to make that decision”, claiming his was the campaign “building the momentum”.