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Congressional Republicans are pushing their leadership to take up legislation that would make it harder for refugees to enter the United States.
The effort comes after two refugees were arrested in the U.S. on terrorism charges.
Sen. Ted CruzTed CruzTrump's America: Businessmen in, bureaucrats out When Trump says 'Make America Great Again,' he means it Booker is taking orders from corporate pharmaceuticals MORE (R-Texas), who is running for president, said the arrests of two Iraqi-born Palestinians raise questions about other refugees already in the country and "what are they planning next."
"There is no doubt we need a retroactive assessment of refugees who have been admitted to this country,” he added in a statement. “We need a comprehensive and thorough review to make sure we are keeping this country safe. And it is my hope that leaders on both sides of the aisle will put aside politics."
Cruz is pushing Senate Majority Leader Mitch McConnell (R-Ky.) and House Speaker Paul Ryan (R-Wis.) to commit to moving three proposals he introduced last year.
The bills would allow governors to reject the resettlement of a refugee into their states; block most refugees coming from Iraq, Libya, Somalia, Syria and Yemen; and remove U.S. citizenship from Americans who join terrorist groups overseas.
Cruz made the request after the Justice Department announced late Thursday that two refugees were arrested on federal terrorism charges.
Omar Faraj Saeed Al-Hardan, who was arrested in Houston, came to the United States in 2009 from Iraq. Aws Mohammed Younis Al-Jayab, who was arrested in Sacramento, came to the United States in 2012 from Syria. Neither has been accused of trying to plot an attack on American soil.
Republicans quickly criticized President Obama in the wake of the arrests. Republican lawmakers have voiced concern that members of terrorist organizations could use the refugee program to sneak into the United States.
Sen. Mark Kirk (R-Ill.), who faces a tough reelection bid, is also pushing for a vote on his legislation that would largely pause the acceptance of Syrian and Iraqi refugees until the administration meets a wide range of requirements aimed at strengthening background checks.
"The terrorism-related arrests of two more Iraqi refugees on American soil proves once again our screening process is weak and needs to be updated," Kirk said in a statement Friday. "This is why the Senate should vote on my bill, the Defend America Act, to give the American people confidence that people allowed into the United States do not have terrorist ties."
While the House passed legislation last year that would halt Syrian and Iraqi refugee acceptance until authorities can verify that terrorists are not trying to infiltrate the refugee population, the Senate has yet to act.
House Homeland Security Committee Chairman Michael McCaul (R-Texas) pushed on Friday for the Senate to take up his measure, saying lawmakers cannot allow "more potential jihadists slip [to] through the cracks."
"They’re ticking time bombs" he told reporters at a press conference Friday. "I don’t know if they were radicalized before they came in or after they came in the United States, but I can tell you they were radicalized terrorists who intended to do us harm."
The House bill, however, likely faces an uphill battle in the Senate, where Democrats say they have the 60 votes needed to block it from moving forward. McConnell is planning to bring up legislation on the refugee acceptance program during the first quarter of 2016, but which bill he will choose is unknown.
Regardless of the Senate's actions, House Judiciary Committee Chairman Bob Goodlatte (R-Va.) said that his committee is working on "several bills to strengthen our immigration programs and enhance national security, including stronger vetting of visa applicants and all refugees."
"We plan to introduce these bills over the coming weeks," he added.
Julian Hattem contributed to this story.