(USA TODAY) -- One Republican senator said Friday that a recently filed immigration bill will need to be looked at carefully now that the FBI believes two immigrants from the Chechnya region were behind the terror bombing at the Boston Marathon.

Sen. Chuck Grassley, R-Iowa, used his opening statement at a Senate immigration hearing Friday to tie proposed changes to the nation's immigration laws to the deadly bombing and ongoing manhunt in Boston.

The FBI says two brothers - Tamerlan Tsarnaev, 26, killed in a gunbattle with police in Massachusetts overnight, and his 19-year-old brother, Dzhokhar - are the main suspects in the blast Monday.

Both are believed to have come to the United States from war-torn Chechnya in 2003, along with other family members, according to the FBI.

Border security is a key component in the sweeping immigration bill that was introduced this week by a bipartisan group of senators. Department of Homeland Security Secretary Janet Napolitano had to postpone testimony she was scheduled to give the Senate on Friday on the security aspect of the bill because of the manhunt for the second brother.

FULL COVERAGE:Boston Marathon explosions

STORY:Latest developments on manhunt for bombing suspect

Grassley said that "in light" of the reports of the immigration background of the suspects, "it's important for us to understand the gaps and loopholes in our immigration system."

But Sen. Charles Schumer, D-N.Y., one of the authors of the immigration bill, cautioned against injecting the tragic events in Boston into the hearing before more was known. He cited the erroneous media reports that claimed the suspects had been arrested two days ago as reason enough to keep Boston out of Friday's hearing.

"This just emphasizes how important it is to allow the actual facts to come out before we jump to any conclusions about Boston," Schumer said.

After the hearing, Sen. Patrick Leahy, D-Vt., said Congress should not overreact to what was going on in Boston.

"If we changed the policies of this country every time something happens - Oklahoma City, 9/11, this - we're never going to do anything," Leahy said. "We should think about what are the best policies for the United States and use those."

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