David M Jackson

USA TODAY

HANAHAN, S.C. — Donald Trump looked to step on a Jeb and George W. Bush rally Monday, and went after Ted Cruz and the Republican Party while he was at it.

Trump calling a news conference just hours before — and a few miles away from — the Bush event, Trump's campaign issued a statement threatening to sue Cruz over his eligibility for the presidency if he does not take down anti-Trump attack ads. He also renewed threats that he could run as a third-party candidate for president.

"I have never ever met a person who lies more than Ted Cruz." Trump told reporters at the news conference.

In the written statement, Trump said: "One of the ways I can fight back is to bring a lawsuit against him relative to the fact that he was born in Canada and therefore cannot be President. If he doesn’t take down his false ads and retract his lies, I will do so immediately."

While he was at it, Trump renewed his threat to run as an independent. He claimed the Republican National Committee is defaulting on its pledge to treat him with respect because of crowds that have booed him during recent debates. "The room has been stacked with special interests and donors," he told reporters. Once the RNC has defaulted on its agreement to treat him fairly, Trump said, he is no longer bound by his pledge to support the eventual Republican nominee.

Cruz, a senator from Texas, was born in Canada, but his mother was an American citizen. In recent weeks, he has campaigned hard against Trump over his past support for Democratic candidates and causes.

Trump said Cruz is lying when he says the businessman would appoint judges who are opposed to Second Amendment gun rights. Cruz has also said that Trump supports abortion rights and government-backed health care.

"It is hard to believe a person who proclaims to be a Christian could be so dishonest and lie so much," Trump said in his statement.

Rep. Steve King, R-Iowa, who has endorsed Cruz, appeared on CNN immediately after Trump’s press conference, calling it a “sickening display of a schoolyard bully.” King said Trump was hurling completely unfounded allegations. “You would never want the president of the United States speaking like that from a podium.”

Cruz said Monday that Trump's attack suggests he is "rattled" because his poll numbers are dropping in South Carolina. In a tweet, Cruz said that "you cannot simply scream 'liar' when someone points out your actual positions."

Trump's indictment also included Jeb Bush, who he says has also produced ads "that in many cases are false."

George W. Bush's decision to campaign for his bother makes him fair game in the campaign, Trump added, repeating his criticism of the former president over 9/11 and Iraq.

Disputing Jeb Bush's claim that his brother "kept us safe" during his presidency, Trump told reporters that 9/11 happened and "the World Trade Center came down during his reign."

Bush said he is tired of hearing Trump attack his family, and that the businessman is not a true conservative.

Trump said he had another reason for wanting to hold a news conference near Charleston: To address concerns that the federal government plans to move prisoners — terrorism suspects — from Guantanamo Bay, Cuba, to the Charleston area.

Pledging to keep the Gitmo prison open, Trump said: "We're not going to let people come here from Guantanamo Bay."

President Obama has pledged to close the prison by the end of his term; some South Carolina lawmakers have expressed concern that some prisoners may be moved to military facilities in their state.