The "absolute limit" will put to consultation, according to the prime minister.
An independent report in 2013 called for a cap on total care costs of £72,000 - a proposal originally backed by the Tories before the 2015 election but subsequently deferred until 2020.
The ruling Conservative party in the United Kingdom is facing a backlash from both voters and party members following the inclusion in the party's election manifesto of controversial changes to how social care would be funded for the elderly.
"Our proposals are that we will refund social care, putting emergency money into it now so those million people waiting for social care don't wait".
Speaking at the launch of the Tories' Welsh manifesto in Wrexham, Mrs May said her manifesto proposals "provide the beginning of a solution to social care without increasing taxes on younger generations".
UK Prime Minister Theresa May's Conservative party has been forced into a humiliating climbdown on a controversial manifesto promise known as the "dementia tax" following sharp criticism of the party's social care policy.
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"Nothing has changed, nothing has changed", she added, with a raised voice.
She insisted that no-one would have to sell their home to pay for care while they were alive and people would still have "something to pass on to" their family after their death.
The U-turn on dementia tax comes after Mrs May repeatedly said she would not hold an early election and after she campaigned for Britain to remain in the European Union.
It is true the Labour leader initially got some of the detail of the policy wrong when he responded on the morning after the Conservative manifesto was published.
But today, in the wake of fierce opposition of what many called "the dementia tax", Mrs May revealed the Tories will introduce the option of a cap on the amount each person must pay for their care.
Under the Conservative plans nobody with assets of less than £100,000 would have to pay for social care.
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Indeed, thanks to the PM's policy of requiring pensioners to contribute more to the costs of in-home care, the weekend was dominated by debate over one of the most pressing policy issues of our time.
The "floor" means people with more than £100,000 in assets will have to pay for their own elderly care out of the value of their homes, rather than relying on the council to cover the costs of visits by care workers.
As now, people's income would also be taken into account when calculating care charges in both settings.
May said the proposed changes to elderly care were part of an attempt to reform the care system for an ageing society.
In a joint statement they said: "Every vote for Labour is a vote for the views and policies of its leader, Jeremy Corbyn".
This comes after analysis by Royal London showed that, under the original plans, those living in London, would on average, have to pay almost four-fifths the value of their home on social care costs before it becomes available for free.
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She said: "This manifesto says that we will come forward with a consultation paper, a government green paper".