NEW YORK—President-elect Donald Trump said he would consider leaving in place certain parts of the Affordable Care Act, an indication of possible compromise after a campaign in which he pledged repeatedly to repeal the 2010 health-care law.

In his first interview since his election earlier this week, Mr. Trump said one priority was moving “quickly” on President Barack Obama’s signature health initiative, which Mr. Trump said has become so unworkable and expensive that “you can’t use it.”

Yet,...