WASHINGTON — House Ways and Means Committee Chairman Kevin Brady on Wednesday suggested that his upcoming tax bill could force changes to 401(k) plans and other retirement accounts, a move that would buck a promise from President Trump that those accounts would be left alone.

The Republican congressman from Texas, speaking at a breakfast hosted by the Christian Science Monitor, said, ‘‘We think in tax reform we can create incentives for people to save more and save sooner.’’

Brady, who’s expected to introduce a tax bill next week, said he was ‘‘working very closely with the president’’ on the issue. He added that many people who have tax-incentivized retirement accounts contribute $200 per month or less, a level he thought was too low.

‘‘We think we can do better,’’ Brady said. ‘‘We are continuing discussions with the president, all focused on saving more and saving sooner.’’

Also Wednesday, Senate Finance Committee chairman Orrin Hatch, a Utah Republican, also said he would oppose Trump’s vow to protect 401(k) plans, but that he was open to changes if they made sense. ‘‘I’m open to look at anything,’’ Hatch said. ‘‘I don’t have any problem looking at everything.’’

He also said he doesn’t feel pressure to change the Senate’s eventual tax bill because of pressure from the White House. ‘‘No I don’t think so,’’ Hatch said. ‘‘He has his point of view, and he may prove to be right in the end. We’ll just have to see. But I’m open-minded about it.’’

Hatch said he hasn’t spoken with Trump about the 401(k) issue since the president sent his directive about it Monday morning.

Trump on Wednesday told reporters ‘‘401(k)s are very important,’’ noting their benefits for the middle class. And while he praised Brady as ‘‘fantastic,’’ he said it was unwise to negotiate on any changes to the tax code’s treatment of retirement plans.

Hatch is the top tax writer in the Senate, and he and Brady have outsized influence over how the tax legislation comes together.

Brady wouldn’t go into any details about how he planned to change incentives to encourage more savings. Rather, he suggested that the current construct of 401(k) accounts and Individual Retirement Accounts was not working well.

These types of accounts allow people to contribute up to $18,000 a year pretax as a way to incentivize saving for retirement. Lowering the tax-free threshold could raise more revenue, but it could also rankle voters. In 2015, more than 50 million Americans had active 401(k) accounts.

Democrats quickly pounced. Oregon Senator Ron Wyden said Wednesday that the 401(k) proposal was an example of GOP lawmakers working to eliminate middle-class tax benefits so they can cut tax rates for the wealthy.

‘‘They cannot keep their hands off your 401(k),’’ Wyden said. ‘‘They can’t help themselves, and you bet we are going to take this to the mat.’’

Brady is planning to introduce his tax bill next week, which Republicans hope will lead to the most sweeping changes to the tax code in more than 30 years. But almost all the key details of the bill remain a mystery. Again and again on Wednesday, Brady said the most pressing decisions have not been reached.