Sen. Rand Paul (R-Ky.) on Monday threw some cold water on the just-begun process of debating new immigration legislation, saying any such push should be delayed until after the country can address why the two suspected Boston bombers were allowed to immigrate to the United States.

"We should not proceed until we understand the specific failures of our immigration system," Paul said in a letter to Senate Majority Leader Harry Reid (D-Nev.). "Why did the current system allow two individuals to immigrate to the United States from the Chechen Republic in Russia, an area known as a hotbed of Islamic extremism, who then committed acts of terrorism?"

Paul added: "The facts emerging in the Boston Marathon bombing have exposed a weakness in our current system. If we don't use this debate as an opportunity to fix flaws in our current system, flaws made even more evident last week, then we will not be doing our jobs."

Although they are of Chechen ethnicity, the brothers immigrated to the U.S. in 2002 from Kyrgyzstan. According to a Washington Post story:

When the brothers were young, the family lived in Kyrgyzstan, a former republic of the Soviet Union in Central Asia, home to a small Chechen diaspora. Dzhokhar, the younger brother, was reportedly born there, although his older brother was born in Russia, according to some news reports....

[Their parents] Anzor Tsarnaev and his wife arrived in the United States in early 2002 after gaining refu­gee status. Their two sons and two daughters followed a short time later with an aunt.

The Senate Judiciary Committee began debating the new immigration bill at a hearing Monday morning, and the debate has already taken a turn for the contentious, with committee chairman Patrick Leahy (D-Vt.) accusing the GOP of trying to "exploit" the Boston bombings to halt immigration reform.

"I urge restraint in that regard," Leahy said. "Refugees and asylum-seekers have enriched the fabric of this country from our founding. . . . Let no one be so cruel as to use these heinous acts of two young men last week to derail the dreams and futures of millions of hardworking people.”

The bill is being pushed hard by Paul's potential rival for the 2016 GOP presidential nomination, Sen. Marco Rubio (R-Fla.).

Paul previously expressed some qualified support for the push on immigration, saying it was something that needed to be addressed and suggesting he agrees with a slightly altered path to citizenship.

Update 1:57 p.m.: Rubio has responded to Leahy and Paul, staking out a middle-ground position that the events in Boston have bearing on the immigration debate, but saying the process should move forward.

“The attack reinforces why immigration reform should be a lengthy, open and transparent process, so that we can ask and answer important questions surrounding every facet of the bill," Rubio said. "But we still have a broken system that needs to be fixed.”