Sens. Ted Cruz and Jeff Sessions said Monday the number of people implicated in radical Islamic terrorist plots in the U.S. has jumped to 113, and they said it’s yet another reason to impose tighter immigration controls.

The senators have been trying to pry loose from the administration the immigration histories of those individuals, saying the public has a right to know how each of them entered the U.S. and what level of scrutiny they got.

The two also added 41 new names to their list Monday, including the two Iraqi refugees who were arrested last week on terrorism-related charges.

“We have now identified an additional 41 individuals, bringing the total to 113 individuals who have been implicated in Islamic terrorism in some manner since early 2014. Of these 113 individuals, at least 14 were initially admitted to the United States as refugees,” the two senators said.

Mr. Sessions, chairman of the Senate’s immigration subcommittee, and Mr. Cruz, one of the GOP’s leading presidential hopefuls, have been prodding the Homeland Security, State and Justice departments for information for months.

They say the information is critical in light of President Obama’s plan to bring 10,000 Syrian refugees to the U.S. this year.

Last week’s arrests have put a focus on the refugee program, with both men having cleared the Iraqi refugee screening process that Mr. Obama says his Syrian program is based on.

But the White House says it won’t change its plans, with officials saying they have faith in the ability of screeners to keep out bad actors.

Mr. Cruz and Mr. Sessions said the problems go beyond the refugee program, and said the pace of immigration from Muslim countries deserves scrutiny.

“The resources spent every year investigating the countless number of immigrant terrorist suspects in the United States are astronomical. And yet, as this costly and dangerous status quo continues, the U.S. continues to admit approximately 680,000 migrants from Muslim countries every five years,” the senators said.

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