Since August, Mr. Pallone and Representative Greg Walden of Oregon, the committee’s top Republican, have pressured Mr. Lighthizer to not include the Section 230-like language in the North American trade deal and the pact with Japan. Mr. Walden said Wednesday said that the high-ranking members were “frustrated” with the administration.

“The 230-like language has no place in a trade agreement,” said Representative Jan Schakowsky, Democrat of Illinois. “This is a gift to Big Tech to insert it in trade agreements.”

Trade officials say that it is their job to help spread United States law around the world and that if Congress does not like those laws, it is their job to change them. The provision’s supporters say that its inclusion in trade deals will not make it harder to alter the law down the road.

“There’s no language in the trade deal that binds Congress’s hands,” Katherine Oyama, Google’s global head of intellectual property policy, told lawmakers. She noted that trade accords frequently include intellectual property protections even though lawmakers regularly debate copyright and patent reforms.

Despite the debate, few lawmakers have introduced legislation to change Section 230. Only one tweak has become law, a controversial measure making it possible to sue platforms when they knowingly facilitate sex-trafficking through content they host. Some lawmakers have questioned whether a similar change should be made to combat the online opioid trade.

On Wednesday, the House lawmakers seemed to have little appetite to throw the rules out entirely. But they were open to changing them.

“I want to be very clear: I’m not for gutting Section 230,” said Representative Cathy McMorris Rodgers, Republican of Washington. “But at the same time, it’s clear we’ve reached a point where it is incumbent upon us as policymakers to have a serious and thoughtful discussion about achieving the balance on Section 230.”