"He made a mistake - he knows it," Giuliani said, adding that Romney should "tell the American people, 'I made a mistake."'
The former New York mayor criticized Romney at a coffee shop in this early voting state a day after his surrogates did the same.
In turn, Romney, in Phoenix to raise money, countered that Giuliani is vulnerable on the tax issue because he challenged a federal line-item veto, and also because he kept a commuter tax in place in New York.
And Sen.criticized them both.
During a debate Tuesday, Romney was asked whether he would seek congressional authorization before taking military action against Iran's nuclear facilities. Romney said he would talk to attorneys, 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."
McCain, who was campaigning in Iowa, criticized Romney's answer, calling it a "product of inexperience. He's not experienced in national security issues."
Romney has called the criticism a "phony issue."
McCain also criticized Giuliani. McCain, a longtime opponent of pork-barrel spending, said a president needs the power to strike unnecessary spending from appropriations bills Congress sends to the White House.
"Interesting in the debate the other night Mayor Giuliani was proud that he fought against and was able to defeat the line-item veto of which I was one of the prime sponsors. I found that fascinating, because no economist will tell you that you're gonna be able to really get rid of these earmarks and pork barrel projects unless you give the president of the United States the same authority that 43 governors have," McCain said. "Frankly, I don't see how you can call yourself a fiscal conservative and be against the line-item veto."
Giuliani challenged the line-item veto in 1997 because it stopped $200 million that was intended for his city. He successfully argued that the power can only come through a constitutional amendment, not through legislation. The Supreme Court stuck down the line-item veto as unconstitutional in 1998.
Giuliani supports such a veto and has promised to seek an amendment that would allow it.
Romney and Giuliani have been clashing more frequently as they try to separate from the rest of the GOP field, but Giuliani also lashed out Thursday at Democratic candidate.
He repeatedly criticized Clinton's spending plans and claimed responsibility for getting her to back off of plan to give every baby born in the United States a $5,000 account to pay for college or a first home.
"We backed her off that - yeah, I try to take credit for that," Giuliani said.
Giuliani said Clinton's initiatives were going to be paid for by raising taxes. "She wants to spend money like George McGovern, and she wants to raise taxes like Walter Mondale," Giuliani said, invoking two past Democratic presidential nominees who did not win the White House.
"I will put more money back in your pocket," said Giuliani, who voted for McGovern in 1972.
At a stop Thursday night in Rock Hill, Giuliani criticized former President Bill Clinton for cutting the military.
"I promise you I'll undo the massive damage that Bill Clinton did to our military," Giuliani said, referring to budget cuts and the so-called peace dividend.
The former New York mayor said the military cuts left the U.S. unprepared, but Giuliani said he wouldn't blame Clinton for the Sept. 11, 2001, terror attacks.
In a speech earlier in the day, Giuliani called for expanding NATO, the trans-Atlantic alliance that has a lead role in trying to revive Afghanistan and stamp out radical groups.
In a speech to NATO leaders in Norfolk, Va., Giuliani mentioned Australia, South Korea, Israel, India, Japan and Singapore as non-European countries that should be considered for membership.
"Many of them cooperate with NATO already in training missions," Giuliani said. "We need their help.
The Bush administration in 2006 proposed an increase in participation and training, but not formal membership, for Australia, South Korea and Japan.