Saying that Christians should not be forced to violate their faith, Republican presidential aspirant Ted Cruz has expressed support for the decision of some counties in Texas to withhold marriage licenses for same-sex couples.

In an interview with the Texas Tribune, Cruz said county clerks in Texas should "absolutely" be given the option not to issue same-sex marriage licenses, even with the Supreme Court's decision legalising gay marriages nationwide.

"We should respect diversity and tolerance. There is this liberal intolerance and fascism that seeks to force Bible-believing Christians to violate their faith, and I think it makes no sense," the conservative lawmaker from Texas said.

He maintained that religious beliefs should still be respected despite the high court ruling on same-sex marriages.

"There's no right in society to force a Jewish rabbi to perform a Christian wedding ceremony. There's no right in society to force a Muslim imam to perform a Jewish wedding ceremony," the senator explained.

Cruz further said that forcing county clerks to issue same-sex marriage licenses although this violates their faith will be tantamount to "religious oppression."

"You look at the foundation of this country — it was to seek out a new land where anyone of us could worship the Lord God Almighty with all of our hearts, minds and souls, without government getting in the way," the Republican presidential aspirant said.

Texas Lt. Gov. Dan Patrick earlier asked Attorney General Ken Paxton to issue a clarification if county clerks and justices can freeze the issuance of same-sex marriage licenses or refuse to perform gay weddings, in the light of a law in the state protecting the free exercise of religious beliefs.

Cruz earlier called the Supreme Court ruling legalising same-sex marriages as "lawless" and called for a constitutional amendment that will allow Americans to vote out high court justices every eight years.