The comments came in a sit-down last week with the editorial board of The State Journal-Register, according
to the Illinois paper's political writer.
"We can't have the president of the United States acting like the drug dealer in chief," Kirk said. "Giving clean packs of money to a ... state sponsor of terror. Those 500-euro notes will pop up across the Middle East. .... We're going to see problems in multiple (countries) because of that money given to them."
Kirk was responding to reports that the administration paid $400 million in cash to Iran in January as Iran released Americans that had been held as prisoners. The money was part of a previously announced settlement in a case stemming from money owed since 1979, but the timing had not been known until this month.
As it denied Republicans' criticism of the exchange as "ransom," the State Department did admit last week that the payment was used as "leverage" to ensure the prisoners' release, and was not given to the Iranians until the individuals were safe.
Kirk has been highly critical of the administration on Iran, including the landmark nuclear deal signed by the two countries last year, comparing it to the appeasement policies toward the Nazis before World War II.
The White House did not respond to a request for comment on Kirk's "drug dealer" remark.
Kirk has stepped into controversy before with his words, some perceived as racially insensitive, including calling
his friend and bachelor Sen. Lindsey Graham, R-South Carolina, a "bro with no ho," adding, "that's what we'd say on the South Side."
Ha also drew criticism when he suggested
black neighborhoods are "one(s) we drive faster through."
Kirk is locked in a tough re-election campaign with Democratic Rep. Tammy Duckworth. His seat is considered one of the most vulnerable in Democrats' bid to retake the Senate majority.
Without addressing the issue of the payment to Iran, the Duckworth campaign called on Kirk to apologize for the remarks on Sunday.
"Sen. Kirk's comments are misguided and deeply offensive, and beneath the dignity of the office he holds," spokesman Matt McGrath said in a statement to CNN. "He should apologize."
The Kirk campaign stood by the comments when asked on Sunday.
"Sen. Kirk was referring to the administration's decision to send pallets of cash, not even US dollars, but euros and Swiss francs, in a clear ransom payment to Iran, the world's leading state sponsor of terrorism," said Kirk campaign manager Kevin Artl. "The decision sets an awful and dangerous international standard that should be investigated and the lack of transparency from the administration clearly indicated they knew their actions were not above board."