Homeland Security Secretary John Kelly told Sen. Rand Paul Wednesday that he would look into reports that U.S. border agents are demanding cellphone data from U.S. citizens and legal residents when they are trying to return home after traveling abroad.

Paul, R-Ky., told Kelly in a Senate Homeland Security Committee hearing that there are reports of thousands of these searches, which he said set an "extraordinarily unreasonable standard."

"We're denying people entry who are citizens or green card holders who are coming back home, and your department is saying to them, you cannot return to your home without giving us your fingerprint, and giving us all of the data on your phone, access to all the data on your phone," Paul said.

Kelly responded by saying he's not aware of any significant increase in searches against U.S. citizens, and said these would normally take place under "very, very, very critical circumstances."

"I would say that an American citizen ought to be able to come back in and not have their electronics searched," Kelly said.

Paul persisted, and said reports say these kinds of searches have increased.

"Let me take that on, senator," Kelly said. He said press reports can often be inaccurate, and that "there's always more to the story."

Kelly later said he believes attempts to download phone data from returning U.S. citizens is "not happening." He said it is "certainly happening to foreigners coming in, "but not routinely."

Paul asked Kelly to get back to him with more information. "Will do," Kelly said.