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Rubio's tweet is in response to Senate Judiciary Committee Chairman Patrick LeahyPatrick Joseph LeahyNSA spying program overcomes key Senate hurdle McConnell to Dems: Don't hold government 'hostage' over DACA Nielsen acknowledges Trump used 'tough language' in immigration meeting MORE (D-Vt.) cautioning lawmakers from rashly connecting comprehensive immigration reform to the Boston Marathon bombing.

"Late last week opponents of comprehensive immigration reform began to exploit the Boston Marathon bombing. I urge restraint in that regard," Leahy said in his opening statement at an immigration reform hearing on Monday. 

Leahy said the immigration bill would improve national security.

"The bill before us would serve to strengthen our national security by allowing us to focus our border security and enforcement efforts against those who would do us harm," Leahy said. "But a nation as strong as ours can welcome the oppressed and persecuted without making compromises on our security. We are capable of vigilance in our pursuit of these values."

A number of lawmakers have said the bombing should be factored into crafting a new immigration reform law. At around the same time that Rubio published his tweet, Sen. Rand PaulRandal (Rand) Howard PaulNSA spying program overcomes key Senate hurdle Fix what we’ve got and make Medicare right this year Despite amnesty, DACA bill favors American wage-earners MORE (R-Ky.) released a letter to Senate Majority Leader Harry ReidHarry Mason ReidDems search for winning playbook Dems face hard choice for State of the Union response The Memo: Immigration battle tests activists’ muscle MORE (D-Nev.) and Senate Minority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellSessions: 'We should be like Canada' in how we take in immigrants NSA spying program overcomes key Senate hurdle Overnight Finance: Lawmakers see shutdown odds rising | Trump calls for looser rules for bank loans | Consumer bureau moves to revise payday lending rule | Trump warns China on trade deficit MORE (R-Ky.), arguing that the effort to overhaul the nation's immigration system should be paused until Congress fully investigates the Boston bombing and adds new protections into the legislation.

In the letter, Paul argued that "the Senate needs a thorough examination of the facts in Massachusetts to see if legislation is necessary to prevent a similar situation in the future."

—This story was updated at 12:21 p.m.