"There’s no religious backing for that," Cruz responded.
Guthrie then asked Cruz whether interracial marriage should be a state issue, even though the Supreme Court ruled that interracial marriage bans are unconstitutional.
"Of course not,' Cruz answered. "We fought a bloody civil war over the original sin of our country, that was slavery. Slavery was grotesque and immoral and some 600,000 Americans lost their lives, spilled their blood on American soil to expunge it."
He said that the 13th, 14th and 15th Amendments honored "the promise of the Constitution."
Texas Attorney General Ken Paxton on Sunday told the state's county clerks that they can refuse to issue marriage licenses to gay couples if they object to same-sex marriage for religious reasons.
Watch the interview via NBC: