The row over providing benefits such as winter fuel payments and free bus passes for better-off pensioners has split the very top of the coalition government, with deputy prime minister Nick Clegg telling colleagues he would be happy to see them dramatically cut.

The Liberal Democrat leader's intervention comes after reports on Wednesday that the work and pensions secretary Iain Duncan Smith is pressing for cuts to the £5bn bill for elderly benefits, which also include free TV licences and prescriptions.

However, David Cameron is said to be adamant that he must stick to the promise he made before the last general election that the payments would be safe under a Tory government, a promise considered important enough to be enshrined in the coalition agreement.

The Lib Dems said in their election manifesto they would delay the politically sensitive winter fuel payments until the age of 65, up from 60, and signalled that they would consider means-testing them. However, Clegg is now understood to be saying he wants to see the winter payments and free TV licences cut for all millionaire pensioners to help fund other government spending – although a party spokesman said they were not seeking to make an issue out of it.

"If you're faced with a choice in terms of helping the wealthiest pensioners or helping the vulnerable across Britain, then his priority is the vulnerable people across the country who need the most help," said a party spokesman.

As well as Cameron's personal pledge in a TV debate before the 2010 election, the government is thought to be nervous about cuts to pensioner benefits after the furore over changes to the rate at which pensions rise announced in the March budget and dubbed the "granny tax".

Ministers are also under fire for delays in getting cross-party agreement on how to fund social care amid concerns that they are preparing to water down proposals by the Dilnot Commission to introduce a cap on total personal costs and to increase the wealth people can accumulate before they have to start paying for their own care.

Pressure is building on the prime minister as departments across government are being asked to make savage cuts to spending while the costs of medical bills and other issues keeps rising.

The Sun launched a campaign to "ditch handouts to [the] rich" on Wednesday, calling on the government to "axe the freebies" for about half of pensioners. The newspaper estimated that would save £2bn a year.

The Lib Dem peer Lord Oakeshott called on the prime minister to accept taxing winter fuel payments, pointing out his party had already had to accept making a major policy U-turn by agreeing to raise student tuition fees, a move which has proved deeply unpopular with its supporters.

Oakeshott has previously calculated that 671 members of the House of Lords qualify for the £200-300 a year handout to help warm their homes because they were over 60. "Nick Clegg had to eat humble pie on tuition fees, so David Cameron can at least swallow a slice now for fairness," Oakeshott said.

A No 10 source said: "The coalition agreement is absolutely clear and it reflects the promises the prime minister made before the election."

A spokesman for the Department for Work and Pensions said: "We continue to protect key support for pensioners including winter fuel payments, which make an important contribution to the fuel costs of pensioners."

• This article was amended on 7 June 2012. The original version wrongly stated that Clegg wanted winter payments and free TV licences cut for all but millionaire pensioners.