Bookies' favourite for the job, Rishi Sunak, was defeated by Ms Truss in the race to become the new PM last month, gathering 60,399 votes to her 81,326.
Tory MP Steve Double said his party should unite behind a candidate such as Mr Sunak.
He added that he was "willing to get behind anyone who will provide the leadership we need, is up to the job and will get back to delivering on the 2019 manifesto we were elected on" Commons Leader Penny Mordaunt said she would "keep calm and carry on" and encouraged others to do the same, in the wake of the PM's resignation.
In the summer campaign, Ms Mordaunt, a Royal Navy Reservist, said leadership "needs to become a little less about the leader and a lot more about the ship".
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