Downing Street has said there are no plans to give further mitigations to pensioners who have lost their winter fuel payment.
Prime Minister Sir Keir Starmer and his cabinet “agreed” on the importance of scaling back the benefit, his spokesperson said.
They said Sir Keir told ministers “tough decisions” were necessary to fix “the foundations of our economy”, at a cabinet meeting.
There is unease among unions and some Labour MPs over the move, ahead of a vote on the policy in Parliament on Tuesday.
The Labour government has a large majority and is expected to win the vote, which has been called by the Conservative opposition.
But with speculation about a potential rebellion by some Labour MPs, the vote will be another early test of the prime minister’s authority, following Labour’s general election win in July.
Conservative leader Rishi Sunak accused ministers of trying to “fast-track cuts” to vital support for pensioners “to fund an inflation-busting pay rise for train drivers”.
He added that Labour MPs “must do the right thing and force the government to come clean about the impact this punishing cut will have”.
Ahead of the vote, Chancellor Rachel Reeves addressed Labour MPs’ concerns at a meeting of the Parliamentary Labour Party on Monday evening.
She told MPs she was “not immune to the arguments that many in this room have made”.
However, she said the government’s commitment to the triple lock meant the state pension had risen by around £900 compared with a year ago.
Ms Reeves added: “It is the right thing to do, to target money at a time when finances are so stretched, at people who need them most.”
Ms Reeves and Sir Keir insist the winter fuel payment cut – worth about £1.5bn – is necessary to fill an alleged £22bn “black hole” in the budget left by the previous Conservative government.
The Conservatives say Labour is exaggerating the state of the public finances to lay the ground for tax rises in the October budget.
The winter fuel payment was a universal benefit, meaning it was paid to all pensioners, regardless of their income or wealth.
The government estimates 9.3 million fewer pensioners will be able to claim the payment of between £200 and £300 a year. Only those on low incomes who receive certain benefits will be eligible.
Charities and many MPs are concerned about those on modest incomes who will miss out.
But the Social Market Foundation think tank says winter fuel payments go to many well-off pensioners who do not need it and have proposed more targeted support for energy bills.
The vast majority of those eligible will only receive the winter fuel payment if they have first claimed pension credit, a state pension top-up.
The prime minister’s deputy spokesperson said the government would “continue to urge people to check their eligibility” for pension credit and to “support people in making those applications”.
The spokesperson said there had been 38,500 pension credit claims in the last five weeks.
In comparison, there had been 17,900 claims over the five weeks before Ms Reeves announced the payment would only be available to those on certain benefits in July.
The PM’s spokesperson said this was a 115% increase, but added the campaign to get pensioners to sign up was “ongoing” and there was “still more to do”.
Dave Stone, from Bournemouth, has been facing a delay with applying for pension credit since 6 February, months before planned cuts to the winter fuel payment were announced, and says the Department for Work and Pensions (DWP) is now “even busier because of the latest changes”.
He applied online to claim pension credit for his aunt, following the council telling him she was eligible, and was given a six-week deadline of 19 March for a response. He said he still does not have an answer seven months later, despite nearly 20 interactions with the team.
“Every time I gave them an extra week or two, then I would call them back after they’d missed their deadlines, and nothing much would happen,” Mr Stone told BBC Radio 4’s PM programme.
“They’ve got to the stage where they’re now even busier because of the latest changes they can’t put anybody through to the pensions centre any more – all they can say is ‘we’ll call you back’ and of course I know [that] isn’t going to happen.”
A DWP spokesman said it had “surged additional staff” to cover the increase in pension credit calls.
Government figures had suggested there were about 800,000 households who were eligible for pension credit but did not claim it.