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Tom Tugendhat, who was on eliminated from the race to replace Boris Johnson on Monday, has not yet said which candidate he will now back.
Pitching himself as the candidate to offer a clean start for the Conservative Party, the backbench MP was widely seen to have performed strongly in the campaign and TV debates before being knocked out of the contest in the third ballot of Tory MPs.
He received 31 votes – the lowest of the remaining candidates – on Monday.
Relying on his record in the Army and his career as a backbencher chairing the Commons Foreign Affairs Committee, Mr Tugendhat offered himself as a candidate untarnished by the scandals that dogged Mr Johnson and his Government.
Mr Tugendhat, who served in the Army Intelligence Corps in Iraq and Afghanistan, also repeatedly mocked his own frequent mentions of his time in the military.
It was apparent on Monday that the Tonbridge and Malling MP would likely fail to reach the final four, with Mr Tugendhat earlier telling the hustings of the backbench 1922 Committee that he was not “naive”.
He said he had rebuffed repeated suggestions he should stand aside to throw his weight behind another candidate.
After his elimination from the leadership contest, Mr Tugendhat said he will listen to what other candidates have to say before deciding who to support.
In a video posted to Twitter, Mr Tugendhat said: “That is the end of the road for me in this race, but look, it has been an amazing run, I’m incredibly proud of the team, I’m incredibly grateful to all the supporters who have been with me at some – if not all – stages of the race we fought for a clean start because we know that that’s what the country is crying out for.
“We’ve seen that in the response to the two debates, we’ve seen that in the engagement we’ve had from people.
“Now I’m going to be with you, of course, over the next two years, fighting in the council elections and then fighting again in the general election and then long into the future, because we need to make sure that our party, the Conservative Party, is able to deliver a clean start for the country and for ourselves.
“But, please, I’m not going to be talking about any candidates at the moment. I’ll listen to what they have to say and I’ll be making my judgment later.”