"If Sen. Rubio were asking me that, I would encourage him, and I do encourage him to get behind Ted Cruz," Lee told reporters.
Lee called Cruz a "close personal friend" and said that while he is the first sitting senator to endorse Cruz, "many" will follow. He asked for the party to unite behind "one leader."
"I expect that I'll be the first of many Republican senators who will endorse Ted Cruz," Lee said. "I'm confident that more are on the way, and I welcome others to join me."
Lee also said that he believes that Cruz would be the best person to nominate a replacement for the late Supreme Court Justice Antonin Scalia, echoing calls from other Republican senators to wait until the next president is elected to choose a Supreme Court nominee.
"That's one of the great things about Ted Cruz is that Americans can proceed with great confidence that Ted Cruz will pick an absolutely outstanding person to fill Scalia's position on the Supreme Court," he said.
Lee and Cruz have been long political allies and aligned during the crusade against Obamacare in 2013 that resulted in a government shutdown.