Damian Green has said Conservatives will not “look again” at plans to fund social care in England, amid warnings they will be unpopular with voters.
The Tory manifesto says elderly people requiring care at home would have to meet the costs but could keep £100,000.
He told the BBC’s Andrew Marr that it would still be “a reasonable inheritance to have”.
But Labour said it would leave people “on their own” and should be pulled.
The Conservatives argue that that is fairer than imposing a £72,000 cap on care costs, which would benefit more those inheriting larger estates.
Four opinion polls for Sunday newspapers suggest that, while the Conservatives retain a big lead, support for Labour has increased over recent weeks.
They put Labour at between 33% and 35%, up significantly on the figures earlier in the campaign, which some polls put as low as 26%.
Conservative think tank the Bow Group has warned that the manifesto pledge on social care costs – which means costs for providing social care at home could now be met from the value of people’s property, after their death, could be the “biggest stealth tax in history” with an “awful” impact on core Tory voters.
But Mr Green told BBC One’s Andrew Marr Show: “The Bow Group is wrong.”
He said that setting a £72,000 cap on care costs funded privately – as previously recommended by government advisor Sir Andrew Dilnot – “meant that the distribution of the benefits became wildly uneven” and argued that their policy was “a better system”.
“It’s got to work for everyone, not just in Ashford and Twickenham, but also in Hartlepool and in north Wales and in Scotland and so on. Allowing everyone to know that there is this flat figure of £100,000 is fair to everyone.”
He stressed a £100,000 inheritance was still “four times as good” as being left with £23,000 – the current threshold over which care costs in residential care must be funded.
“Everyone knows there will be a decent inheritance for them, nobody will have to lose their home during their lifetime or the lifetime of their surviving spouse.”
Mr Green said there would be a green paper covering both social care and health “coming out in the summer”.
But Shadow Chancellor John McDonnell said a cap on privately funded costs – rather than a “floor” – was a better system.
“What we want to make sure, just like the NHS, is there is pooled risk so everybody is certain.
“That’s why we supported Dilnot but we also supported a cross-party approach because we have got to have something that is sustainable over generations.”
Under the Conservative plans nobody with assets of less than £100,000 would have to pay for care, including everything from help washing and dressing, through to round-the-clock support.
Currently anyone with assets of over £23,250 is expected to pay the full cost of their residential care and the value of your house can be taken into account.
But that is not the case if you receive care in your own home. Under the Tory plans the value of your home may be factored in, although the money will not be taken from your estate until after death.
This means some people could face losing their home after they die and will not be able to pass it down to their children.
The policy was defended by Foreign Secretary Boris Johnson on ITV’s Peston’s Politics.
He called it a “sensible, grown-up Conservative approach” to dealing with the “massive problem of the cost of social care”.
But added the detail will be consulted on and worked out.