Video report by ITV News Political Correspondent Emily Morgan
The prime minister is facing pressure from her top ministers to ease up on austerity, with some suggesting the issues of public sector pay, schools funding and university tuition fees should be considered.
Environment Secretary Michael Gove has urged the government to listen to the findings from independent bodies that review public sector pay.
He told the Sunday Times: "You've got to listen to the public sector pay review bodies.
"When they made recommendations on school teachers' pay I think I always accepted them.
"My colleagues who deal with these pay review bodies would want to respect the integrity of that process."
Mr Gove also told the BBC's Andrew Marr Show: "These pay review bodies have been set up in order to ensure that we can have authoritative advice on what’s required, in order to ensure the public service on which we rely are effectively staffed, and the people within them are effectively supported."
It comes after a week in which Labour criticised the government for initially raising, then playing down hopes that the current cap, which is due to remain in place until 2019/20, could be lifted.The government remains under pressure after losing its House of Commons majority in the General Election as Jeremy Corbyn's anti-austerity Labour outperformed expectations.
Mr Gove's intervention ties in with reports that Health Secretary Jeremy Hunt is to demand a wage boost for NHS workers.
According to the Observer, Mr Hunt is to demand an end to the 1% pay cap for nurses and other health workers, citing evidence from the government's own NHS pay review body published in March
Education Secretary Justine Greening is also demanding an extra £1 billion to protect schools funding per pupil and will demand a statement in weeks, the Sunday Telegraph reported.
A Number 10 source said the government was responding to the recommendations of public sector pay review bodies which are currently reporting to ministers "on a case-by-case basis".
The source said the pay cap was brought in to "deal with the mess we inherited from Labour" and acknowledged the "hard work and sacrifice" made by public sector workers, saying jobs had been protected and the deficit reduced by three quarters.
"While we understand the sacrifice that has been made, we must also ensure we continue to protect jobs and deal with our debts," the source added.
They also made clear there are no moves to change tuition fee policy after Mrs May's most senior minister, Damian Green, said student debt was a "huge issue" and a national debate may be needed on the issue.
Answering questions after a speech calling for Tory modernisation to win over young voters, Mr Green said acknowledged that student debt was a "huge issue".
Meanwhile, speaking at an anti-austerity "Tories out" demonstrationin central London on Saturday, Mr Corbyn attacked the Tories for their "shambles" over the pay cap earlier in the week.
He also accused the party of "hypocrisy", linking the issue to the Grenfell Tower disaster.
"The utter hypocrisy of government ministers and others who queued up in the chamber over there in the House of Commons to heap praise on the emergency services, the following day to cut their wages by refusing to lift the pay cap.
"The hypocrisy is absolutely unbelievable."