This article is more than
8 year oldMr Trump, who has pledged repeatedly to repeal the 2010 law, signalled he was receptive to a compromise after visiting the White House on Thursday.
He told the Wall Street Journal he favours keeping two pillars of the bill because "I like those very much".
One is a ban on insurers denying coverage for pre-existing conditions.
The other provision that the president-elect told the newspaper he favours allows young adults to be insured on their parents' policies.
Mr Trump told the Journal it was his hour-and-a-half meeting with Mr Obama that had made him reconsider his calls for an all-out repeal of the Affordable Care Act.
"I told him I will look at his suggestions, and out of respect, I will do that," the president-elect said at Trump Tower.
"Either Obamacare will be amended, or repealed and replaced."
The interview was published just as Mr Trump shook up his presidential transition team, demoting New Jersey Governor Chris Christie to vice-chairman.
"Repeal and replace" - with emphasis on the former over the latter - has been the Republican mantra when it comes to Barack Obama's healthcare reform for the past six years. Candidate Donald Trump echoed this when he labelled the programme a "disaster" and promised something much better if he were elected president.
Just days after the US public gave Mr Trump the keys to the Oval Office, however, he said there are parts of Mr Obama's signature legislative achievement worth keeping.
The challenge for the president-elect is that the Obamacare features he praises - such as its mandate that insurers cover pre-existing medical conditions - are made possible by portions of the law he has condemned, like requiring all Americans to obtain insurance.
Keeping the law's carrots while abandoning its sticks could prove difficult.
Complicating the matter is that a "revise and reform" effort may not fly with Mr Trump's ardent supporters and the cadre of arch-conservative politicians in Congress, who want to tear up the law "root and branch".
Mr Trump often broke with Republican orthodoxy while campaigning and didn't pay a political price. He may learn that as president he won't get far without his party establishment's help.
During the election campaign, Mr Trump said the government-run health insurance marketplace was "a total disaster" and "a catastrophe".
"Obamacare is just blowing up," he said only last month, while promising his own plan would deliver "great healthcare at a fraction of the cost".
While running for president, Mr Trump did not offer much detail on what he envisaged would be Obamacare's replacement.
The Republican's plan included tax-deductible health savings accounts and allowing insurers to sell coverage across state lines.
His apparent change of heart on Friday comes amid a surge in applications to join the plan from Americans possibly fearful it is about to be overturned.
More than 100,000 applicants snapped up Obamacare health insurance on the day after Tuesday's election, this year's biggest sign-up, the Obama administration announced.
About 22 million Americans would be without insurance if the law was repealed.
Congressional Republicans have voted more than 50 times to undo the law.
Though the Republicans have maintained control of the Senate, they cannot repeal the Affordable Care Act in its entirety because under senate rules, the Democratic minority remain in a position to block the move.
The Republicans could, however, starve parts of the bill of funding through a budgetary process called reconciliation.
The law has not been without its difficulties.
Last month, the Obama administration said the average cost of medical coverage under the bill was expected to rise by 25% next year for those Americans who do not qualify for subsidies.
And about one in five consumers would only be able to pick plans from a single insurer, it added.
Former President Bill Clinton last month called the unsubsidised portion of the law "the craziest thing in the world".
Unlike in many other Western countries, the US does not have a single-payer healthcare system.
Private companies, rather than the US government, provide health insurance for US citizens.
Newer articles
<p>The two leaders have discussed the Ukraine conflict, with the German chancellor calling on Moscow to hold peace talks with Kiev</p>