The former Minister of Defence also stretched further for Liz Truss.
In the second ballot Suella Braverman crashed and lost five supporters, while Mrs Mordaunt picked up 16 additional supporters.
The Secretary of International Trade received 83 votes in the contest to replace Boris Johnson.
Former Chancellor Rishi Sunak remains the leader with 101 supporters, up from 88 in Wednesday’s first round of voting.
He said he was “incredibly grateful” for the support of his colleagues after the second vote.
“I am willing to give everything I have in the service of our nation,” he added.
“Together we can restore confidence, rebuild our economy and reunite the country.”
Tom Tugendhat lost support and received 32 endorsements compared to 37 on the first ballot.
But he said he would not withdraw from the competition and would participate in the scheduled TV debates, scheduled for Friday, Sunday and Monday.
“The campaign for #ACleanStart continues,” he tweeted.
“Thank you to all my friends and colleagues who have pledged their support.
“We need confidence in our politics again. I will present my vision for Britain to the public during the TV debates next week.”
The results:
Rishi Sunak: 101 (got 13 votes)
Penny Mordaunt: 83 (got 16 votes)
Liz Truss: 64 (got 14 votes)
Kemi Badenoch: 49 (got 9 votes)
Tom Tugendhat: 32 (5 votes lost)
Suella Braverman: 27 (Away)
Two Tory MPs did not vote.