His remarks -- including his comment that he was persuaded by Obama earlier in the week to take another look at maintaining some of the program -- came as he has appeared to hedge on other campaign promises just days after winning the presidency.
Here's a look at a few other areas where President-elect Trump is seemingly backing away from Candidate Trump.
Trump has previously called Obamacare a "disaster." But, he told the Wall Street Journal
, "I told him I will look at his suggestions, and out of respect, I will do that."
In an interview with CBS' "60 Minutes" that aired later Friday, he specifically talked about the need to continue coverage for individuals with pre-existing conditions.
"Yes, because it happens to be one of the strongest assets," Trump told Leslie Stahl.
Trump also said he'd try to keep the measure that allows young people to stay on their parents' insurance plans until age 26.
"We're going to very much try to keep that. It adds cost but it's very much something we're going to try to keep," Trump said.
Trump's openness to compromising on Obamacare, however, was complicated Friday by a shift in the official positions listed on his website.
The Washington Post reported
that Trump has revised his health care agenda to steer it more in line with Republican Party orthodoxy.
The paper said the presidential transition website has been edited to now include allowing health care workers to not perform acts that would violate their religious or moral beliefs and to "protect innocent human life from conception to natural death."
The paper also said the website omits Trump's call to allow Americans to import prescription drugs from other countries where they are sold at lower prices.
During the second presidential debate, Trump interrupted Hillary Clinton by threatening to appoint a special prosecutor to investigate -- and convict -- the Democratic nominee over her use of a private email server.
His campaign rallies were also marked by chants of "Lock her up" as supporters clamored for Trump to jail his opponent.
Speaking to the Journal, however, Trump seemed to be less committed to the idea.
"It's not something I've given a lot of thought, because I want to solve health care, jobs, border control, tax reform," he said.
Earlier in the week, top Trump surrogates Rudy Giuliani and Chris Christie also seemed to back away from the idea
Trump drew outrage last year when he called for a "shutdown" of Muslim immigration to the US. He later amended the plan, calling for "extreme vetting" and a shutdown on immigration from countries compromised by terrorism, but he never refuted his original policy and in July called the new iteration of his plan an "expansion" of his original Muslim ban.
Appearing on Capitol Hill Thursday to discuss his legislative agenda, Trump was asked by a reporter if he would "ask Congress to ban all Muslims from entering the country."
Trump appeared to hear the question but walked away after thanking everybody.