CHICAGO (AFP) - Republican White House hopeful Ted Cruz faced a legal challenge to his eligibility to be president on Friday in a lawsuit filed over his birth in Canada.

It comes after frontrunner Donald Trump - a "birther" who famously challenged President Barack Obama to produce his Hawaiian birth certificate - has been hammering away at the hardline Texas senator's eligibility.

Cruz insists he has met the constitutional requirements to be a "natural-born" citizen because his mother was born in Delaware.

During a presidential debate on Thursday night, he accused the real estate mogul of manufacturing a crisis to retain his lead in the polls.

"Back in September, my friend Donald said he had his lawyers look at this from every which way and there was no issue there," Cruz said.

"Now since September, the constitution hasn't changed. But the poll numbers have," he added. "Donald is dismayed that his poll numbers are falling in Iowa."

He went on to point out that Trump, whose mother was born in Scotland, was disqualifying himself.

Trump shot back: "As you know, Ted, in the last three polls I'm beating you. So you shouldn't misrepresent how well you're doing with the polls."

"You have a big lawsuit over your head."

The lawsuit filed in federal court in Texas is seeking a judgment on Cruz's eligibility, arguing that the case law is simply not clear on the definition of a natural born US citizen.

"The entire nation cannot afford such constitutionally (sic) confusion and uncertainties overhangings (sic) the electorate process," the suit filed on behalf of Texas resident Newton Boris Schawtz argues.

Cruz was born in 1970 in Calgary, Alberta to an American mother and a Cuban father who returned to live in the United States after a year. Cruz renounced his Canadian citizenship last year.

In 2008, a man unsuccessfully challenged the eligibility of Republican contender John McCain, who was born on a US military base in Panama.

As a precaution, the Senate unanimously adopted a resolution recognising McCain as a natural citizen.

The lawsuit noted that despite the fact that Obama's mother, like that of Cruz, was indisputably an American citizen, his eligibility remains in doubt among conservative critics who still believe he was actually born in Kenya, the country of birth of his father.

"It was his birth in Hawaii that was decisive and not his mother's," the lawsuit contends. "That is why it has been under constant attack for eight years, including by Donald Trump publicly."