US Republican presidential hopeful Donald Trump and his top challenger Ted Cruz have clashed over Cruz's Canadian birth and the business tycoon's "New York values" during a tense debate.

With the February 1 nomination ballot in Iowa, a swing state coming into sharp focus, the debate on Thursday was a key one to influence voters, who will start to pick the party's nominee to run for the White House in November.

Texas Senator Cruz, who was born in Calgary, Alberta, to a US citizen mother and a Cuban father, accused Trump of bringing up his birthplace simply because Cruz was leading some polls in Iowa.


READ MORE: Republican debate scorecard


Cruz said Trump, who led the movement questioning whether the Hawaiian-born President Barack Obama was really born in the US, had asked his lawyers to look into the issue of Cruz's birth in September and concluded there were no issues.

"Since September, the Constitution has not changed but the poll numbers have," Cruz said.

"And I recognise that Donald is dismayed that his poll numbers are dropping in Iowa, but the facts and the law here are really clear."

Call to go to court

Trump said Democrats would sue if Cruz were on the Republican ticket, putting their party's chances of winning at risk.

I am not going to be taking legal advice from Donald Trump.

Ted Cruz, Texas governor

He urged Cruz, who is a lawyer, to ask a court to put the question to rest.

"I am not going to be taking legal advice from Donald Trump," Cruz retorted.

Trump has been making an increasing issue of Cruz's Canadian birth, suggesting it violated the constitution's requirement that only "natural born citizens" can be president.

The business tycoon openly accepted in the debate that he was bringing the issue up because Cruz was doing better in the polls.

In addition to fighting back over his presidential eligibility, Cruz accused Trump of not being a conservative because he was born in New York and still lives there.

"Everyone understands that the values of New York City are socially liberal, are pro-abortion, are pro-gay marriage," Cruz said.

Cruz in rise

The top seven candidates ranked by Republican voters took part in the debate: Trump, Cruz, Florida Senator Marco Rubio, retired neurosurgeon Ben Carson, former Florida Governor Jeb Bush, New Jersey Governor Chris Christie and Ohio Governor John Kasich.

Cruz has taken the lead in some polls of Iowa Republican voters. A victory at the debate could propel him higher in the national race.

Inside Story - What does Trump stand for?

The other candidates sought to gain traction in the debate with criticism of Obama's policies on gun control and also threw barbs about his State of the Union address on Tuesday.

In that speech, Obama sought to offer a more optimistic vision for the US's future, and he singled out Trump, without naming him, for calling on the US to ban Muslims temporarily from entering the country.

Bush urged Trump to change his views on the issue. Trump, who noted that his poll numbers rose after making that policy proposal, said his mind was made up.

A Reuters/Ipsos rolling national poll on January 12 showed Trump had 39 percent of the vote, Cruz 14.5 percent, Bush 10.6 percent, Carson 9.6 percent, while 6.7 percent favoured Rubio, once viewed by the Republican establishment and many donors as a rising star.

Source: Agencies