Downing Street has signalled that it is ready to review the 1% cap on public sector pay rises.
A senior Number 10 source said Prime Minister Theresa May had "heard the message" from the General Election that voters were "weary" of austerity.
He made clear ministers were ready to consider upcoming recommendations from public sector review bodies, which could bust the long-standing cap, and that the issue would be up for review in Chancellor Philip Hammond's Autumn Statement.
Labour described the move as "very encouraging", pointing out that it came ahead of a Commons vote on an opposition amendment to the Queen's Speech calling for an end to the pay cap.
Asked about the future of the pay cap, the Downing Street source said: "Ministers, including the Prime Minister and the Chancellor, have been clear that we are going to listen to the messages that were sent at the election.
"We understand that people are weary after years of hard work to rebuild the economy.
"Public sector pay restraint is one of the tough choices we've had to make to balance the books after Labour's crash and what was left behind. We are working through and looking at recommendations from pay bodies that are coming."
Rehana Azam, national officer of the GMB union, said: "Public sector pay cuts were always a political choice.
"Theresa May has been forced into this position because of her reduced majority, but the GMB won't stop campaigning until public sector workers have had a proper pay rise.
"The devil will be in the detail – all public sector workers must now receive an above inflation pay rise, including those not covered by a Pay Review Body such as council workers, school support staff and police staff.
"This is one Theresa May U-turn we welcome, but our members won't take the Government's word for it."
Public and Commercial Services union general secretary Mark Serwotka said: "If this is a sign of the Government beginning to see sense we welcome it, but any review must include all public sector workers and lead to the cap being lifted for all of them. Nothing else will be acceptable.
"Theresa May has no mandate and no authority to continue with this policy that has caused misery for millions of workers."
Public sector workers have seen the value of their incomes fall in relation to inflation after two years of pay freezes and four years of annual caps since 2010.
Former chancellor George Osborne announced a further four years of 1% caps in the 2015 budget, leaving rises well below prices in a period when inflation has risen to 2.9%.
Previous recommendations from pay bodies which bust the cap have been ignored by ministers.
The amendment tabled by Labour leader Jeremy Corbyn calls for the cap to be scrapped in order to give emergency workers and other public servants "a fair pay rise".
A senior Labour source said: "I think it is clear that one of the results of the election and the very sharply increased Labour vote and number of seats and the fact that this is now a minority government means that they have had to make a number of important concessions to the public.
"They have retreated on the winter fuel allowance, they've abandoned their attempts to scrap the triple-lock on pensions and now they appear to indicate that they are going to review the public sector pay cap, which obviously we were calling for during the election campaign."
Answering questions following a speech at the Royal United Services Institute in London, Defence Secretary Sir Michael Fallon was asked whether service personnel could expect above-inflation pay rises.
He replied: "That is a huge question. It is partly a matter for the pay review bodies but it also involves a forecast of where you expect inflation to be.
"I think we expect inflation to start falling back again from the autumn onwards. This is something we have to consider, not just for the Army but right across the public sector as a whole."
Transport Secretary Chris Grayling told the BBC's Daily Politics: "We have had to take some tough decisions and in the wake of the General Election we are going to have to think through what we do come the next Budget."
Tory former minister Sir Oliver Letwin acknowledged there was a case for "easing up" on austerity but warned a "large number" of people may be required to contribute more in tax to pay for any increase in public spending.
While the better-off would "bear a larger share of the cost", tax rises could not be limited only to the very rich, he said.
Sir Oliver told BBC Radio 4's Today programme: "It may well be that, in one way or another, a large number of people will have to pay a little more tax if we are going to maintain the trend towards reduced deficits and yet spend a bit more on the crucial public services that do need more spending."
TUC general secretary Frances O'Grady said: "It's about time that hard-working public sector workers got they pay rise they've earned.
"If the cap is lifted, it will be a massive victory for trade union campaigning.
"But this can't be kicked into the long grass, it needs to happen now. Public sector workers have waited long enough."
Unison general secretary Dave Prentis said: "This review is a step in the right direction.
"But the Government has to commit to ending the pay cap and not use the review as a stalling tactic. Ministers must also recognise the impact of the wage freeze on public sector employees, and on the services they provide.
"It's clear that austerity isn't working. Public sector staff have waited long enough and won't tolerate any more delays."