Top Republican presidential rivals Donald Trump and Ted Cruz continued bashing each other, with Trump questioning his rival's Christian faith on Friday.

"How can Ted Cruz be an evangelical Christian when he lies so much and is so dishonest?" the real estate magnate wrote on Twitter.

This was apparently in response to a Cruz attack ad accusing Trump of having "a pattern of sleaze stretching back decades," the Business Insider reported. The political ad focused on Trump's support for eminent domain, or the government's power to seize private property.

This was the second time that Trump had raised doubts on Cruz's Christian tag. In December, when he started attacking Cruz, Trump brought up his rival's Cuban ancestry which he linked with his faith.

"To the best of my knowledge, not too many evangelicals come out of Cuba, OK? Just remember that, OK? Just remember," Trump said at a December rally in Iowa.

Aside from his attack on Cruz's faith, Trump is also threatening to sue the Texas senator over his eligibility to run for president, WND reported.

"If [Ted Cruz] doesn't clean up his act, stop cheating, & doing negative ads, I have standing to sue him for not being a natural born citizen," Trump tweeted Friday.

Trump has been raising questions on Cruz's eligibility since January, warning that in case Cruz wins the Republican nomination, the Democrats may file lawsuits challenging his ability to serve as president in a general election.

Cruz, a constitutional lawyer and former solicitor general of Texas, has maintained he is eligible to run and serve as president, pointing out the distinction between natural-born and naturalised citizens.

Cruz may have to formally state his case in court as voters in Alabama filed a lawsuit last Feb. 3 asking a district court to declare that Cruz is "ineligible to qualify/run/seek and be elected to the Office of the President of the United States of America," due to his Canadian birth, The Hill reported Friday.

The lawsuit cites Article II, Section 1 of the Constitution, which states, "no person except a natural born citizen, or a citizen of the United States, at the time of the adoption of this Constitution, shall be eligible to the office of president."

Under that clause, the plaintiffs claim, "Cruz is not a 'natural-born' citizen of the United States of America."

"Mr. Cruz was born in Canada, and obviously Canada is not a territory or protectorate of the United States, it's not dominion of the United States," Thomas Drake, counsel to the plaintiffs, told the Hill.

"And as such, when he was born, at the moment of his birth, location determined his status, and his status was that of a natural-born Canadian citizen," Drake said, adding, "You cannot be a natural-born or native-born citizen of two countries."