TALLAHASSEE, Fla. – The vice presidential candidates took their debate over Iraq and domestic issues from one battleground state to another yesterday, Vice President Cheney contending that the Democrats have been “on the wrong side” of national security issues for years while Senator Edwards claimed the Republicans are “in denial about everything.”

Messrs. Cheney and Edwards traded jabs over jobs, judgment, and Iraq in what largely was a hard-fought draw Tuesday night in Cleveland. As they campaigned yesterday in Florida, post debate polls were split over who came out ahead, but each side claimed victory in the battle for momentum.

President Bush joined the argument in Wilkes-Barre, Pa., where he told cheering supporters that Democratic presidential candidate John Kerry didn’t understand the war on terror and proposes policies that would weaken the country and make the world more dangerous.

With Mr. Kerry in Englewood, Colo., preparing for the second presidential debate tomorrow, Mr. Edwards carried the Democratic ticket’s criticism of Messrs. Bush and Cheney – “the same old tired ideas, the same old false attacks, the same old tired rhetoric” – from Ohio to Florida. Both states are likely to determine the winner of the November 2 election.

Mr. Edwards said Messrs. Bush and Cheney won’t acknowledge “the mess in Iraq” or trouble with jobs and the economy.

“You can’t fix these problems until you recognize there is a problem,” Mr. Edwards said in West Palm Beach, Fla. “They’re in denial. They’re in denial about everything.”

For his part, Mr. Cheney questioned whether the Democratic challengers are capable of sustaining the war on terrorism.

“John Kerry and John Edwards cannot with tough talk obscure a record that goes back 30 years that had him on the wrong side of virtually every issue that dealt with national security,” Mr. Cheney told a rally in Tallahassee.

Mr. Bush offered a sharp if familiar critique of his rivals, accusing Mr. Kerry of wavering in his support of the war on terrorism, favoring scores of tax increases, and sending mixed signals to allies and enemies. He even offered an explanation for the scowls and grimaces he displayed during the presidential debate last week in Miami when Mr. Kerry criticized nearly every action the president has taken on national security, taxes, education, and health care.

“You hear all that you can understand why somebody would make a face,” Mr. Bush said.

Messrs. Bush and Kerry will meet again Friday night at Washington University in St. Louis to take questions from voters. After the vice presidential debate at Case Western Reserve University in Cleveland, the Bush camp claimed that a strong performance by Mr. Cheney helped break momentum that appeared to be going Mr. Kerry’s way. Democrats said Edwards more than held his own.