Florida Sen. Marco Rubio has been under increased security the past three weeks after a possible threat to his life was uncovered by the U.S. government, CBS Miami confirms.

CBS Miami has obtained a memo detailing the threat, written by a federal agency, and sent to local law enforcement through the Department of Homeland Security. CBS Miami agreed not to show the memo and to not cite names, locations or identifying information. The Miami Herald first reported the memo on Sunday.

The two page memo is marked "law enforcement sensitive" but does not appear to be classified.

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The U.S. became aware of a "possible threat against Florida United States Senator Marco Rubio" and refers to a "potentially grave threat to Sen. Rubio."

The memo says the threat comes from Diosdado Cabello, a top Venezuelan lawmaker who is a former top military official. However, the memo stresses the information concerning the possible assassination plot is not corroborated.

Rubio is known for being a harsh critic of the Venezuelan regime. Last month, Rubio called Cabello the "Pablo Escobar of Venezuela."

Rubio has been under increased security the last three weeks or so, beginning in Washington and now in South Florida.

"The U.S. Capitol Police [USCP] is responsible for the security of members of Congress. It would be inappropriate for DHS to comment on the seriousness of the threat. However, Federal Protective Service (FPS) and USCP collaborate regularly and have processes in place to share information and, as applicable, process requests for assistance. USCP has not requested assistance at this time," DHS spokesman Dave Lapan said in a statement to CBS News.

CBS News' Andy Triay contributed to this report.