The authors of the Senate immigration bill are mounting a campaign to try to make sure the Boston Marathon bombings last week don’t derail their push to overhaul the U.S. immigration system, saying the problems lie more with the FBI than with legal immigration.

In the wake of the revelation that the two men suspected of the bombings were immigrants, some on Capitol Hill said it should be a reason to slow down enactment of an immigration reform bill.

But Sen. Charles E. Schumer, New York Democrat and one of eight senators who wrote the immigration legislation, said they won’t accept a delay.

“There are some, some on the hard right, some otherwise, who opposed our immigration bill from the get-go, and they’re using this as an excuse. We are not going to let them do that,” Mr. Schumer said Sunday on CNN’s “State of the Union” program. “We’re not going to let them use what happened in Boston as an excuse because our law toughens things up.”

At stake is a fundamental disagreement over whether legalizing illegal immigrants and allowing more legal immigration makes the U.S. safer or endangers it.

Sen. Lindsey Graham, South Carolina Republican and another co-author of the bill, said legalizing the estimated 11 million illegal immigrants will help weed out people with terrorist intentions and let law enforcement focus on real threats.