Among other things, the bill would have allowed religious officials to abstain from performing same-sex marriages, if doing so would have violated their religious beliefs.
The senator from Texas also presented himself as a serious alternative to GOP front-runner Donald Trump in the increasingly personal and heated Republican primary.
“Who cares what Donald is tweeting late at night? We need real solutions for the real problems in this country,” said Cruz, referring to the mogul's proclivity for launching attacks on social media.
Asked about Trump's threat of a lawsuit over delegate allocation in Louisiana, Cruz replied: "Who cares. He can threaten whoever he likes. I think the American people are getting tired of it."
Just to show you how unfair Republican primary politics can be, I won the State of Louisiana and get less delegates than Cruz-Lawsuit coming— Donald J. Trump (@realDonaldTrump) March 27, 2016
Cruz also commented on a petition that circulated online to allow firearms to be openly carried at the Republican National Convention in Cleveland. The Secret Service on Monday vetoed the possibility, saying that only law enforcement will be allowed to carry guns at the summer gathering. When asked about it, Cruz didn’t pass judgment on the petition but he said it was appropriate to defer to the Secret Service.
"I haven't reviewed the particular petition," Cruz said. "I will say, at the convention the Secret Service is going to have the principal decision-making concerning security and so that you would certainly want to get the recommendation from Secret Service -- how to maintain security for everyone."