Sir Desmond Swayne, representative for New Forest West, spoke out after news emerged on Friday of an apparent plot to oust Mrs May from Number 10.
He said: "She was chosen [to be Prime Minister] and she won an election. She got the highest share of the Conservative vote that we have had in 25 years, almost going back to Margaret Thatcher's post-Falklands election."
The supposed attempt to eject Theresa May is being led by former Tory Party chairman Grant Shapps (pictured above). He claimed to have the backing of around 30 MPs.
Mr Shapps told BBC Radio 4's Today programme: "They are Remainers, they are Brexiteers. A growing number of my colleagues, we realise that the solution isn't to bury our heads in the sand and just hope things will get better.
"It never worked out for Brown or Major and I don't think it is going to work out here either."
Sir Desmond said he believes Mr Shapps had not requested his support because Mr Shapps knew he would have been sent away with "a flee in his ear".
The Dorset MP added: "I'm certainly in support of the Prime Minister.
"We have a difficult task ahead and we need to concentrate entirely on that task; on managing the public finances and, at the same time, negotiating our way out of the European Union."
In her first public appearance since her Conservative Party Conference speech - which was marred by a bad cough, a prankster and faulty backdrop on stage - the Prime Minister said she had the "full support" of her cabinet and insisted she will keep providing "calm leadership".
Asked whether he felt there was significant appetite among Tory MPs for Mrs May to quit, Sir Desmond responded: "I did a trawl of colleagues back in July.
"I couldn't find anyone who was in favour of a leadership contest and I really don't think that would have been altered by a frog in the prime minister's throat."
Click here to listen to Premier's Alex Williams speaking with Sir Desmond Swayne: