Republican U.S. presidential candidate Donald Trump threatened Friday to sue rival Ted Cruz over his eligibility to serve as president in the event Cruz does not “clean up his act.”

Trump made the threat in a tweet that marked the latest escalation of a rapidly growing fight between the two GOP candidates. The billionaire businessman from New York and the U.S. senator from Texas have been going back and forth for weeks, trading increasingly hostile barbs as they head toward the South Carolina primary election this month.

Trump previously brought up the issue of Cruz’s citizenship, recalling the so-called birther conspiracy theories he trumpeted about President Barack Obama back in 2011 when Trump was mulling a 2012 presidential run. Unlike Obama, who was born in Hawaii, Cruz was not born in the U.S. He was born in Canada to an American mother and a Cuban father.

Most legal experts have agreed the American citizenship of Cruz’s mother makes him a natural-born citizen. The U.S. Constitution says, “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.” The constitutional requirement has been debated by some scholars, but Cruz, who is a constitutional lawyer and the former Texas solicitor general, maintains he is eligible to be president.

When the topic came up during previous Republican presidential candiate debates, Trump pledged he would not file a lawsuit against Cruz, but warned that Democrats would do so. “I’m not bringing a suit,” Trump said at a debate in January. “I promise. But the Democrats are going to bring a lawsuit.”

Trump’s threat was made after a group of his supporters filed a federal lawsuit challenging Cruz’s eligibility to run for the White House, the Hill reported Friday. Before threatening the lawsuit Friday, Trump had been tweeting complaints about Cruz’s campaign tactics. The businessman accused the senator of running push polls, which are surveys designed to negatively influence respondents’ opinions about a particular candidate.

Trump also described Cruz using a vulgar word at one of his rallies, and he has criticized his rival for running advertisements that he considers too negative. Cruz launched ads this week that describe Trump as buying influence “in a pattern of sleaze stretching back decades.” The two men will get another chance to face each other during the Republican presidential candidates debate in South Carolina Saturday night.