U.S. House Speaker Nancy Pelosi, a Democrat from California, center, speaks during an event with House and Senate Democrats on protecting the Affordable Care Act outside the Supreme Court Building in Washington, D.C., on Tuesday, April 2, 2019.

Pelosi's cautionary comments come after President Donald Trump reignited the health-care debate when the Department of Justice decided to support a federal judge's ruling that Obamacare is unconstitutional. Republicans have vowed to do away with Obamacare since it became law in 2010, but have been unable to do so.

Pelosi told the Post on Thursday that she would rather work to improve the Affordable Care Act, also known as Obamacare, and doesn't know if Medicare for All could deliver what it has promised.

In an interview with The Washington Post published this week, House Speaker Nancy Pelosi challenged a health-care proposal touted by many Democrats, questioning if the "Medicare for All" bill will be able to supply as much coverage as the Affordable Care Act.

Many on both sides of the aisle say the GOP's failed effort to repeal Obamacare in 2017 was a driving force behind the party's loss of 40 House seats in last year's midterms that gave Democrats a majority in the chamber.

On Thursday, Pelosi said she's "agnostic" on Medicare for All. She added that she believes when most people say they want Medicare for All, they really mean that they want health care for all. She said many enjoy the employer-based benefits they receive under Obamacare, which they would lose if Medicare for All becomes law.

"Show me how you think you can get there," she told the Post. "We all share the value of health care for all Americans -- quality, affordable health care for all Americans. What is the path to that? I think it's the Affordable Care Act, and if that leads to Medicare for All, that may be the path."

The concept of single-payer health care became more mainstream after Sen. Bernie Sanders, I-Vt., made it a prime focus during his unsuccessful run for president in 2016. The Medicare for All bill proposed by Sanders, who is again running for president in 2020, would create a national health insurance program that covers every U.S. citizen.

Many other presidential candidates, including Sens. Kamala Harris, D-Calif., Cory Booker, D-N.J., Elizabeth Warren, D-Mass., and Kirsten Gillibrand, D-N.Y., support Medicare for All and signed on to Sanders' legislation in 2017. Lawmakers in the House also showed support for universal health care after more than 100 Democratic members signed on to a single-payer bill unveiled by by Rep. Pramila Jayapal, D-Wash., in February.

Pelosi is not alone in her reluctance to support Medicare for All. Republicans and other Democrats warned that millions of people would lose their employer-based health care under the proposed bill.

Sanders' office did not immediately respond to CNBC's request for comment on Pelosi's statements.

Pelosi, who was instrumental in passing Obamacare during her first speakership in 2010, also wondered if Medicare for All would be too expensive, noting that it currently has a $30 trillion price tag.

"Medicare is not as good a health benefit as the Affordable Care Act," she told the Post. "So, if you are to do Medicare-for-all you have to improve the package — and when you improve the package, you have to have more money."

Pelosi's office did not immediately respond to CNBC's request for additional comment.

Read The Washington Post's full report here.