Trump explained in an interview with The Wall Street Journal published Friday that his shift came after White House talks Thursday with Obama, who asked him to consider preserving parts of the Affordable Care Act.
"Either Obamacare will be amended, or repealed and replaced," Trump told the newspaper.
"I told him I will look at his suggestions, and out of respect, I will do that."
Trump's repeated attacks on the law were a central focus of his campaign, during which he used it to needle rival Hillary Clinton as insurance premiums rose for some enrollees, especially in battleground states.
But, while the ACA has faced unanimous Republican opposition since its enactment in 2010, the question of they could replace it has remained unanswered. About 20 million Americans have gained health insurance under the law, reducing the share of the public without coverage to below 10 per cent, the lowest level recorded.
According to The Journal, Trump said he favored maintaining a prohibition on insurance companies denying consumers coverage based due to so-called pre-existing conditions. Before the law took effect, insurers had been able to refuse to cover people who had previously suffered almost any illness.
Trump also said he was not opposed to requiring insurers to allow children to remain on their parents' insurance policies until the age of 26, a key Obamacare tenet.
Republican lawmakers have previously said they favor such policies.
The law is a flagship achievement of Obama's presidency and he vetoed Republican legislation last year which would have gutted central provisions of it, such as eliminating programs and subsidies that ensure coverage for poor and lower income Americans.
The Congressional Budget Office found in 2015 that the Republican measure would have increased the number of people without insurance by 22 million, a large share of whom would be children. The measure would have reduced government spending in the short term but resulted in a budgetary drain beginning in 2026.
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