Billionaire businessman Donald Trump has raised more questions about Ted Cruz's eligibility to serve as US president, telling his rival that his birth in Canada leaves "a big question mark on your head".
Thursday's Republican Party debate - the first of the year - came less than three weeks before the Iowa caucuses kick off this year's voting.
Mr Trump has led the Republican field for months, confounding Republican leaders and many of his rivals. "You can't do that to the party," he told the Texas senator.
But Mr Cruz forcefully defended his ability to serve as president. He suggested Mr Trump was only turning on him because he is challenging Mr Trump's lead, particularly in Iowa, which kicks off voting on February 1.
"The Constitution hasn't changed - but the poll numbers have," Mr Cruz said. The senator was born in Canada, but his mother is American, which legal scholars agree fits with the Constitution's provision that only a "natural born citizen" may be president.
The heated exchanges signalled an end to months of relative civility between Mr Trump and Mr Cruz, both of whom are appealing to Republican voters deeply frustrated with Democrats in Washington and sometimes with their own party leaders.
Mr Cruz renewed his criticism of Mr Trump's "New York values," a coded questioning of Mr Trump's conservatism that elicited an unexpectedly emotional response from the real estate mogul about the city's response to the September 11 2001 attacks.
"No place on earth could have handled that more beautifully, more humanely than New York," Mr Trump said. "That was a very insulting statement that Ted made."
Mr Cruz also defended his failure to disclose loans of some 1 million dollars from Wall Street banks on federal election forms during his 2012 Senate campaign, saying it was little more than a "paperwork error".
Underscoring the split in the party that has defined the turbulent Republican primary, the more mainstream candidates on stage fought to edge their way into the debate.
On the economy and national security, the candidates offered a sharp contrast to the optimistic portrait of the nation President Barack Obama outlined in his State of the Union address earlier this week, warning that sticking with Democrats in the November election could have dire consequences.
"On Tuesday night, I watched story time with Barack Obama, and it sounds like everything in the world was going amazing," New Jersey governor Chris Christie said.
On national security, former Florida governor Jeb Bush suggested the country was less safe under Mr Obama and declared Hillary Clinton, the Democratic front-runner, would be a "national security disaster".
Florida senator Marco Rubio went even further, saying Mrs Clinton was "disqualified for being commander in chief," accusing her of mishandling classified information and lying to the families of Americans killed in the 2012 attacks in Benghazi, Libya.
Mr Rubio likened Mr Christie's policies to Mr Obama's, particularly on guns and education reform - an attack Mr Christie declared false. Seeking to undermine Mr Rubio's qualifications for president, Mr Christie suggested that senators "talk and talk and talk" while governors such as himself are "held accountable for everything you do".
Mr Trump stuck with his controversial call for temporarily banning Muslims from the United States because of fear of terrorism emanating from abroad. He said he had no regrets about the proposal and noted that his poll numbers rose after he announced the plan.
Republicans have one more debate scheduled before voting begins in Iowa.