- Video report by ITV News Correspondent Angus Walker
Chancellor Philip Hammond has told ITV News that Tory MPs should "stick with" Theresa May amid reports that some are calling for a leadership contest.
Some Conservative MPs have grown frustrated with the prime minister and troubles within the Government, including the approach to Brexit negotiations.
It has been reported that the number of MPs who have written to the chairman of the backbench 1922 Committee calling for a leadership contest is close to the trigger point needed to force one.
But asked by ITV News Business Editor Joel Hills about disquiet within the party over Brexit, he replied: "I would say to my colleagues, stick with the prime minister.
"She's doing this in a very careful and methodical way. She's navigating a very tricky, difficult negotiation process. We have to get an implementation period agreed, then we have to negotiate the best possible deal for Britain for the future relationship with the European Union.
"I have confidence in the Prime Minister to deliver that and I would urge them to get behind her."
Brexit Secretary David Davis also moved to play down reports of bad feeling between cabinet members in a speech saying the top team were working together to deliver the best result for all sides.
"There is no difference between the Chancellor and myself and indeed the Prime Minister in terms that we both want a Brexit that serves the British economy and serves the British people," he said.
"There will be arguments about the tactics but they will change, the options available to us will change throughout the course of the negotiations."
However, Mrs May is facing open criticism from some of the more staunch supports of a hard Brexit.
Prominent Brexiteer Jacob Rees-Mogg, who chairs the influential Tory European Research Group, warned on Thursday of the May administration taking a "timid and cowering" approach to EU withdrawal.
And a usually loyal MP Mark Pritchard, went public to speak out about "growing frustration" among his colleagues at Westminster.
Concerns have been voiced by backbenchers over the competence of the Number 10 operation, following the botched snap election of 2017, Mrs May's ill-fated conference speech and a poorly-received reshuffle.
There have also been complaints of Mrs May failing to listen to views of backbenchers.
One Tory MP, speaking on condition of anonymity, told the Press Association: "David Cameron was aloof, but exercised patronage with precision to great effect.
"Theresa May is aloof but has no clue how to exercise patronage and as a result is rapidly alienating many Tory backbenchers, even some of her friends."
Contacted by the Press Association, Sir Graham refused to comment on how many letters he had received.
But committee insiders denied suggestions that he has resorted to urging Tory MPs to hold off from demanding a contest because he is close to the threshold for triggering one.