Mitt Romney made a “big mistake” when he said he would consult lawyers before taking military action on Iran, Rudy Giuliani told FOX News on Wednesday.

Giuliani and Romney, who faced off over several issues during Tuesday's Republican presidential primary debate, continued their battle through the media on Wednesday in a series of statements on the campaign trail and through their respective spokesmen.

Speaking at an editorial board meeting with FOX News in Washington, D.C., on Wednesday, Giuliani said Romney's so-called mistake showed that he doesn't understand the role and authority of the president of the United States.

“I can’t imagine John F. Kennedy during the Cuban Missile Crisis … saying ‘I will check with lawyers,’” Giuliani said. “It was one of those moments" when he covered his mouth in shock over his opponent's response.

Responding to a hypothetical question about whether he would seek congressional action prior to involving the U.S. militarily with Iran, Romney said at the debate Tuesday: “You sit down with your attorneys and tell you want you have to do, but obviously the president of the United States has to do what's in the best interest of the United States to protect us against a potential threat."

Giuliani said he thinks Romney’s statement was a major faux pas that may come back to haunt him.

“The American people are looking for leadership. This isn’t a time to check with lawyers,” Giuliani said, adding that during crises like the one on Sept. 11, 2001, the last thing a president should be doing is checking with attorneys. The former New York City mayor said he attempted to immediately respond to the Romney statement during the debate but did not get recognized.

Needling Romney further, Giuliani's camp compared the former Massachusetts governor to 2004 Democratic nominee John Kerry. In a statement titled, "Romney's Lawyers Test For National Security," the Giuliani campaign lambasted Romney.

In another statement on the same theme, the campaign wrote: "Going to war is the most serious decision a president can make. ... Lawyers should not debate while our national security is on the line. In these momentous decisions, we need leadership, not litigation."

For his part, as he campaigned in Michigan on Wednesday, Romney called the rhetoric by his chief rival about his answer a “phony issue."

"I made it very clear. ... I'd make a decision based on the safety of the American people. But of course we'd also check to make sure what our legal and constitutional responsibilities are."

The former Massachusetts governor also took a dig at Giuliani's litigious leanings, saying, "If there's somebody that wants to talk about suing and lawyering, the mayor gets first place."

Romney cited the former New York mayor's lawsuit against the line-item veto and other cases he filed while mayor. The issue followed Tuesday's exchange between the two over which candidate was more fiscally responsible.

During that exchange, Romney claimed he cut taxes during his one term as governor and quoted a Club for Growth finding that spending went up 2.2 percent annually under Romney, but 2.8 percent during Giuliani's two terms as mayor. He then added that the best tool to keep spending down is with a line-item veto, a device that tax-cut proponents say would help reduce spending, and Romney said he used 847 times.

Giuliani noted during the debate that the U.S. Supreme Court had ruled that the line-item veto is unconstitutional for the federal government, and he prosecuted the case because former President Bill Clinton wanted to use that illegal authority to cut funding for New York City.

In response on Wednesday, Romney said Giuliani will sue just about anyone who disagrees wit him.

"The mayor's the one who sued Governor (George) Pataki to keep the commuter tax in place. It's the mayor who sued the government of the United States over the line-item veto ... How many times has he sued? " Romney asked. "He's sued the gun manufacturers, he's sued the president."

Katie Levinson, Giuliani's communications director, retorted that perhaps the value of a case is most evident by the attorney who files it.

"Hopefully, Mitt Romney isn't going to check with the same group of lawyers who told him the Bill Clinton line-item veto was constitutional," Levinson said.

FOX News' Serafin Gomez, Shushannah Walshe and Mosheh Oinounou contributed to this report.