The government is ready to accept the key recommendation of a report on support for elderly people and cap the total amount individuals are expected to pay for personal care in their old age, the health secretary indicated on Sunday.

But Andrew Lansley made clear that no decision had been made on the level of the cap beyond which the state would pick up the care bill.

The health secretary said he expected to give a "very positive" response to the report of the Dilnot commission on the future funding of care and support when it is presented on Monday.

Economist Andrew Dilnot's central recommendation is expected to be an overall cap of between £30,000 and £50,000 on the total amount any individual has to pay for care – at an estimated cost to the exchequer of £2bn or more a year.

He believes this would save thousands of pensioners from having to sell their homes to pay for residential care, and would enable insurers to offer cover for the potential cost of personal care.

Experts suggest companies could offer insurance to cover care costs of up to £50,000 for a one-off premium of around £17,000.

Dilnot's commission is also expected to recommend a more generous threshold for means-tested assistance from the state, which currently goes only to those with assets worth less than £23,250.

Charities have issued a call for all-party talks to ensure that reform is not kicked into the long grass, and David Cameron and Labour leader Ed Miliband have both said they are ready to take part in discussions of this kind.

Miliband on Saturday wrote to Cameron and his deputy, Nick Clegg, offering to put aside Labour's proposals for a levy on the estates of the deceased to pay for care – derided as a "death tax" by Tories – in order to seek cross-party consensus.

In an interview with the Sunday Telegraph, Miliband said he had written to the Conservative and Liberal Democrat leaders to offer talks "in good faith", with no preconditions.

The Labour leader wrote: "In return, I hope you both will show the same kind of leadership of your parties as well. The last thing Britain needs is for Andrew Dilnot's proposals to be put into the long grass. We three party leaders are of similar age and the same generation. This is a once-in-a-generation opportunity which our generation must address."

Lansley said that he would also like to see charities and representatives of elderly people and their carers contribute to the debate on the Dilnot recommendations.

The health secretary – who said he had not yet read the report – told BBC1's Andrew Marr Show: "I think we are going to give a very positive response. We are going to treat it as the basis for engagement."

But he added: "Andrew Dilnot's commission makes clear that there is a range of issues within their own report that need to be resolved and on which it is fair for people to be able to express their view: where a cap should be set; how it is to be paid for; issues with the threshold for the means test; how the means test should be applied to people in the future, so they contribute to the cost of their care. And of course if people are in residential homes, they raise the question of the extent to which they should pay for their accommodation costs – as it were, their 'hotel' costs in residential homes."

Lansley made clear that keeping the status quo was not an option.

"We will not be able to give people the quality of care and support and the sense of security that they need in the future unless we have change," he said.