Mrs May said there would be a cap limiting the amount that people will need to pay for care in their own home.
Speaking in Wales, she insisted this had always been the plan. But no such cap was promised in the Conservative election manifesto published less than a week ago.
Abandoning a manifesto pledge in the middle of a general election campaign undermines Mrs May's claim to offer "strong and stable" leadership.
It follows the announcement that a Tory government would require people receiving social care in their own home, including people with dementia, to pay for it through the value of their property.
At the moment, people with significant assets such as money in the bank are already expected to pay - but the value of their home is not included when their assets are calculated.
In practice, the policy set out in the manifesto would mean that many family homes have to be sold once a person receiving care dies. Although they could stay in the home as long as they live, the inheritance they leave their children might be dramatically cut.
But introducing a cap on the amount people have to pay - the change announced by Theresa May - would reassure people that they will still able to leave a significant sum to their children.
It means the Conservatives have announced a u-turn on a manifesto pledge before the election has even taken place.
The Conservative plan already allowed people to stop paying for care once their assets fall below £100,000.
Mrs May said that Labour leader Jeremy Corbyn had misled people about the Conservative plans, and pointed out that the Government was due to hold a consultation about the proposals - something that governments do with almost any new policy.
She said: "This manifesto says that we will come forward with a consultation paper, a government green paper.
"And that consultation will include an absolute limit on the amount people have to pay for their care costs."
U-turn comes after polls showed fall in Tory support
Labour had dubbed the policy a "dementia tax", on the grounds that it meant people with dementia have to pay while those receiving long-term care for other medical conditions might not.
And opinion polls showed the gap between Labour and the Conservatives narrowing - with the social care policy apparently playing a role in reducing the Tory lead.
Polling company Survation put Theresa May's party on 43 per cent and Labour on 34 per cent, a lead of nine points for the Conservatives and significantly down on earlier polls.
And the survey found people were more likely to say Labour had the best policies for older people and the NHS.
Labour brings dementia tax campaign to Birmingham
In a sign that Labour feel the "dementia tax" is highly unpopular, Labour Shadow Health Secretary Jonathan Ashworth was focusing on the policy as he visited the marginal seat of Birmingham Erdington today.
He visited Erdington Medical Centre with Jack Dromey, Labour’s parliamentary candidatefor Birmingham Erdington to speak to Doctors and patients about the social care crisis and the knock-on impact on health services.
Mr Ashworth said: " It’s the Tories who have pushed social care into crisis; their cuts to councils have meant £4.6bn axed from social care budgets between 2010 and 2015, leaving 1.2 million people struggling to get by without care.
"We face a social care time bomb – and making people pay for their own care visits will not help to address this long-term national crisis.
"Jack has been a brilliant local campaigner on these issues, urging the Chancellor to address the growing gap that Birmingham faces in its health and care provision. People are being let down and the Tories can’t say they weren’t warned."
UKIP slams Tory social care "death tax"
UKIP has called the policy a "death tax".
UKIP economic spokesman Patrick O'Flynn said: "This Tory death tax could involve taking tens of thousands or even hundreds of thousands of pounds out of someone’s estate if they have been unlucky enough to suffer an extended debilitating condition late in life.
"This is a Russian roulette approach to paying for social care for the elderly and the abrogation of government responsibility. It makes a mockery of the claims of Mrs May and her key advisers to be running a communitarian Conservative administration."
Lib Dems join attack on "dementia tax"
And Tim Farron, Leader of the Liberal Democrats, launched what he called a national movement calling on people, irrespective of their party affiliation, to stop the "dementia tax".
Writing to the leaders of leading health and older peoples’ charities, he said: "The measure of a Government is how they treat the most vulnerable in our society. I don’t think that the Conservatives are unaware of the impact of their plans but they chose to ignore the human cost.
“Every elderly person that needs care should receive it in the best place for them and not be fearful of those mounting, limitless costs. I am determined that we ensure that Theresa May drops the so-called ‘Dementia Tax’ and implement a cap on the cost of care.
“Caring for our elderly must be above party politics and that is why I want to urge anyone who opposes the Conservatives’ plans to come together to stop it."