Rubio never mentioned Cruz by name during his remarks on a stage set up on an indoor basketball court. But he criticized Republican lawmakers who voted to change the nation's intelligence gathering policies.
"We have to have the ability to know more about them than they ever know about us," Rubio said of the terrorists. "And that's why we have to have strong intelligence programs. It is unacceptable that today because of disclosures and because of changes to the law, supported sometimes by Republicans themselves, we have lost the ability to find these people before they find us."
Rubio has criticized Cruz for his support of the USA Freedom Act, which placed greater limits on government surveillance. Cruz has been hitting Rubio on immigration, accusing him of supporting "amnesty" as a member of a bipartisan group of senators who pushed comprehensive reform in 2013.
The clash is taking on increasing influence in the campaign as Cruz and Rubio rise in the polls.
Cruz's campaign put out a press release on Tuesday that said Rubio is "wrong" to attack him on national security, and it added that he is "proud to stand with conservatives" in support of the USA Freedom Act.
Rubio told the crowd here, which his campaign estimated was more than 750 people, that the Islamic State is motivated by a "perverse interpretation of their Sunni faith." He called them "radical Islamic terrorists," using a label President Obama has refused to apply to them.
"We have not spent enough time educating the American people about who ISIS is," said Rubio, using an acronym for the Islamic State.
Alabama is one of several Southern states that will vote on March 1 as part of the so-called "SEC primary." Rubio's trip here, which also included a fundraiser, came amid a busy week of campaigning. He made two stops in New Hampshire on Monday and campaigned in South Carolina Tuesday morning.
Rubio kicked off his remarks with a good-natured jab at the many University of Alabama football fans in attendance. Alabama plays Florida, where Rubio attended college, in Saturday's SEC championship game. Alabama is a heavy favorite.
"I will make you this guarantee right now: You will not cover the spread," quipped Rubio.