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But human rights advocates say that would be a mistake.

Erol Kekic, director of the Church World Service’s immigration and refugee program, said there are situations where someone wants to return home to see a dying relative or to try to play a role in constructive politics. And then there are the situations where someone was granted asylum years before, but their home country has since stabilized.

“If we’re going to deny protection for people like that I think that’s really taking away from any common sense,” Mr. Kekic said.

He said it wasn’t even clear whether Homeland Security officials could track every person they suspected of returning to their home countries.

“I really don’t think this is practical in any way, nor is it effective. I just think it’s politically motivated, and that’s unfortunate,” he said.

Meanwhile, the committee has already approved one amendment from Mr. Grassley that would crack down on another part of the Boston saga.

Asamat Tazhayakov, one of three men accused of hiding evidence on behalf of the accused bombers, was readmitted to the U.S. earlier this year even though his student visa had expired. The visa information wasn’t shared with frontline Customs and Border Protection officers at the airport, who admitted him without knowing he should have been denied.

The committee unanimously adopted an amendment that requires information in the Student and Exchange Visitor Information System be available to all border protection officers at ports of entry.