Poe said that under current law, the Department of Homeland Security is required to report to State when countries refuse to take their citizens back from the United States. However, he said, Homeland Security "does not always enforce the rule of law."

Poe's bill would correct that by giving countries 90 days to take back their citizens in these deportation cases, and if not, all diplomatic visas would be withheld. Other visas could also be withheld under the bill, which Poe said would apply primarily to Cuba, Iran, Pakistan and China.

"Our good buddies the Chinese are the second-worst offenders, with 35,000 convicted criminals pending deportation," Poe said. "Imagine that — Chinese criminals in the United States. Who would have thought?"

The Deport Convicted Foreign Criminals Act, H.R. 3256, was introduced with seven Republican co-sponsors.