"Many of these individuals are not vetted," Blackburn told CNN's Brianna Keilar.
Keilar corrected Blackburn, noting that refugees who come to the US go through an extensive vetting process.
It can take up to two years for a Syrian refugee to get admitted to the US, State Department spokesman John Kirby told CNN after the interview, and 80% of those already here are women and children.
Asked for specific examples of refugees who went around the official process and were still granted access into the country, Blackburn pointed to the office of refugee resettlement and reception centers.
"When there is someone and they don't know who they are, or where they are coming from, they don't let them in," Keilar said.
Blackburn responded: "But there's not certainty and specificity into that process."
According to Kirby, the departments of State, Homeland Security and Defense, the Federal Bureau of Investigation, The National Counterterrorism Center, the Terrorist Screening Center and the intelligence community all participate in the vetting process.
"The US Refugee Admissions Program employs teams of highly-trained DHS officers who travel overseas to interview and screen each individual applicant for refugee admission in a process that is comprehensive, well-ordered and highly deliberative," he said. "Whenever in any doubt, DHS denies a refugee's application and they are not permitted to travel to the US."
Blackburn, a Republican congresswoman from Tennessee, is a long-time supporter of President-elect Donald Trump. During his campaign, Trump famously called for a ban on Muslims from entering the US as a response to terrorism. He has since called for a ban on individuals from terrorist-prone countries and has called for "extreme vetting," though he has not yet outlined the terms of such a ban.
Blackburn's remarks come amid a week of two terror attacks, one in Turkey and another in Berlin.