A group of Senate Republicans wants to largely pause the acceptance of Syrian and Iraqi refugees until the administration meets a wide-range of hurdles aimed at bolstering background checks.

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Kirk also wants the DHS inspector general and the comptroller general of the United States to, separately, review the certifications and give their findings to Congress and for DHS to give a quarterly report to Congress on the number of refugees who tried to enter the United States and how many were given certifications.

Kirk's legislation would also require the FBI, the DHS and the Director of National Intelligence to clarify within six months how the administration plans to enhance its screening for refugee applicants, including reviewing social media. He also wants to know if any changes were made after two al Qaeda supporters entered the United States in 2009 as Iraqi refugees.

The Illinois Republican, who is facing a tough reelection in a blue-leaning state next year, has repeatedly backed a pause in the acceptance of refugees since the attacks.

He criticized Rep. Tammy Duckworth (D-Ill.), who is running for the Democratic nomination to take on Kirk next year, during a TV ad earlier this month, saying she "wants to bring 200,000 Syrian refugees to America even though the FBI says they cannot be safely screened."

"The refugee screening process was significantly enhanced. Refugees are the most carefully vetted of all travelers to our country," he said in a letter to the editor in the State Journal-Register on Monday. "During this holiday season, I hope more political leaders will take the time, as I have, to meet Syrian refugees living in Illinois."

Kirk's legislation would also crackdown on the Visa Waiver Program while prioritizing visas for Iraqi and Afghan translators.