The Tonbridge & Malling MP secured the requisite votes on Thursday to make it through to the next ballot, beating Attorney General Suella Braverman who crashed out of the competition.
Mr Tugendhat, who is standing to replace Boris Johnson after the PM said he would step down last week, received the backing from 32 MPs to make it into the next round of votes.
Former Chancellor Rishi Sunak received the most votes on Thursday with 102, followed by Penny Mordaunt with 83, Liz Truss with 64 and Kemi Badenock with 49 – all remain in the leadership race.
Mr Tugendhat who has never held ministerial office but chairs the Commons Foreign Affairs Committee, has promised the UK a ‘clean start’.
The former army officer how had served in Afghanistan and Iraq had also pledged to spend 3 per cent of gross domestic product (GDP) on defence and security.
The next round of voting is due on Monday, with subsequent rounds if required until two candidates are left, who will then battle it out over the summer to win the support of Conservative members, with their choice of the next prime minister being unveiled on September 5.
Mr Johnson will then formally tender his resignation to the Queen to make way for his successor the following day.
After earning 32 votes, Tom Tugendhat said he will take part in the upcoming TV debates and put forward his “vision for Britain”.
“The campaign for #ACleanStart continues,” he tweeted.
“Thank you to all my friends and colleagues who have pledged their support.
“We need trust back in our politics. I will be putting my vision for Britain forward to the public at the TV debates next week.”
Two TV debates will happen next week, hosted by ITV and Sky News.
The first Tory leadership debate will take place on Sunday, July 17, followed by another debate on Monday, July 18.