When asked if Rubio should drop out, Lee said: "Everyone will have to make that choice. If Senator Rubio were asking me that, I would encourage him, and I do encourage him to get behind Ted Cruz."
Lee waited months to make his endorsement, and said Thursday was the right time.
"I was waiting, looking for the right moment when it was time to unite," he said.
When asked if he considers Donald Trump a conservative, Lee said he doesn't "think I can make that determination based on the information that he’s given us so far."
Cruz is not well-liked among his Senate co-workers, but Lee is an exception. Lee backed a Cruz-sponsored bill on domestic surveillance last year; Rubio has said during the course of the presidential campaign that the bill endangered national security, and Lee has defended Cruz.
But Cruz and Lee have broken ranks. Cruz said that a criminal justice reform bill Lee sponsored could have dire consequences and release violent offenders from prison.
Lee's office and Cruz's campaign declined comment.
Kelsey Snell contributed to this report.