Vice President Cheney, a Washington veteran, and Senator Edwards, a freshman in Congress, clashed repeatedly last night over Iraq, the war on terror, and their personal political track records. Their 90-minute debate in Cleveland saw both parties’ running mates fiercely trading barbs as they sought to boost their tickets.

Neither gave ground in the only scheduled vice presidential debate of the election campaign. The Democratic senator from North Carolina belied his nickname of “Mr. Nice” and set the tone quickly by turning to the vice president and bluntly accusing him of “not being straight with the American people” about Iraq. The vice president challenged Mr. Edwards’s Senate record and dismissed it as not being distinguished, and said Senator Kerry did not have “the qualities needed to be commander in chief.”

The sharpness of the face-off between the men, which contrasted with the collegial nature of Mr. Cheney’s debate four years ago with the Democratic nominee for vice president, Senator Lieberman, hardly let up after the initial smiles and handshake.

In answering the first question about Iraq, Mr. Cheney insisted the world is safer today because of the war and the capture of Saddam Hussein. If he had it to do all over again, the vice president said, he would recommend that America invade Iraq and remove Mr. Hussein from power.

“The effort that we’ve mounted with respect to Iraq focused specifically on the possibility that this was the most likely nexus between the terrorists and weapons of mass destruction,” he said. “The biggest threat we face today is the possibility of terrorists smuggling a nuclear weapon or a biological agent into one of our own cities and threatening the lives of hundreds of thousands of Americans. What we did in Iraq was exactly the right thing to do.”

Mr. Edwards responded: “It’s not just me that sees the mess in Iraq. There are Republican leaders, like John McCain, like Richard Lugar, like Chuck Hagel, who have said Iraq is a mess and it’s getting worse. And when they were asked why, Richard Lugar said because of the incompetence of the administration.”

He condemned the administration as not having a plan to win the peace. “They also didn’t put the alliances together to make this successful,” Mr. Edwards said. “We need a fresh start.”

The senator said the vice president was misleading Americans when he sought to connect Mr. Hussein with the September 11 terror attacks.

“I want the American people to hear this very clearly,” he said. “Listen carefully to what the vice president is saying – because there is no connection between Saddam Hussein and the attacks of September 11th – period. The 9/11 Commission has said that’s true. Colin Powell has said it’s true. But the vice president keeps suggesting that there is. There is not.

“And, in fact, any connection with Al Qaeda is tenuous at best,” Mr. Edwards said of Mr. Hussein.

Mr. Cheney said the senator was wrong.

“I have not suggested there’s a connection between Iraq and 9/11, but there’s clearly an established Iraqi track record with terror,” he said. “And the point is that that’s the place where you’re most likely to see the terrorists come together with weapons of mass destruction, the deadly technologies that Saddam Hussein had developed and used over the years. Now, the fact of the matter is, the big difference here … is they are not prepared to deal with states that sponsor terror.”

The two argued over basic facts several times, with Mr. Edwards saying America is shouldering 90% of the casualties in Iraq and has spent $200 billion. Mr. Cheney shot back that America was sustaining only 50% of the casualties, with Iraqis and allied troops making up the other half, and he accused the senator of demeaning the Iraqi effort.

“For you to demean their sacrifice is beyond the pale,” he said to Mr. Edwards, who was seated a few feet away.

“Oh, I’m not,” the Democrat protested before the vice president cut him off.

Mr. Cheney also took issue with the $200 billion figure and said Mr. Edwards had failed to acknowledge financial support from other countries, including the writing off of an Iraqi debt amounting to $80 billion.

“It wasn’t $200 billion, but you probably weren’t there to vote for that,” the vice president said, taking a swipe at Mr. Edwards.

“Frankly, senator, you have a record that’s not very distinguished,” Mr. Cheney said to the North Carolina lawmaker, after accusing him of a pattern of absences in the Senate during his one term. He said later: “Your rhetoric, senator, would be a lot more credible if there was a record to back it up.”

Mr. Edwards challenged his opponent over the multibillion-dollar postwar contracts awarded to Halliburton, the firm Mr. Cheney once ran. The vice president looked irritated at one point, denied any wrongdoing, and said the allegations were aimed at obscuring the Democratic candidates’ “undistinguished” record on foreign policy. Incidentally, the Kerry-Edwards campaign gave a front-row seat in the audience to Senator Leahy, a Democrat to whom Mr. Cheney directed a slur earlier this year after an altercation over Halliburton on Capitol Hill.

The two candidates also clashed on the current situation in Afghanistan, with Mr. Cheney saying the upcoming elections showed that the country had seen “enormous progress” since the ousting of the Taliban regime. Mr. Edwards said insecurity in Afghanistan was still rife, that 75% of the world’s opium was being cultivated there, and that most of the country was in the hands of warlords.

In the latter part of the 90-minute debate, the candidates clashed over the economy, health care, and education. Mr. Cheney accused the Democrats of seeking to raise taxes. Mr. Edwards said the Republicans had cut taxes for millionaires only.

At only one point during the debate was the tone less than sharp. In a question about same-sex marriage, Mr. Edwards mentioned a daughter of Mr. Cheney’s who is a lesbian. “I think the vice president and his wife love their daughter,” Mr. Edwards said. “I think they love her very much, and you can’t have anything but respect for the fact that they’re willing to talk about the fact that they have a gay daughter, they’re willing to embrace her.” The vice president declined to engage Mr. Edwards on the subject, simply thanking him for “his kind words about my family.”

Later in the debate, the vice president appeared to wrong-foot his rival, who seemed to expect Mr. Cheney to criticize his pre-Senate work as a highly successful personal injuries lawyer. When asked about caps on medical malpractice awards, Mr. Cheney said he wanted them but did not take up moderator Gwen Ifill’s characterization of Mr. Edwards as “part of the problem.” Mr. Edwards also seemed prepared to be accused of lacking experience for the vice presidency, but Mr. Cheney avoided that attack line. Cheney aides said that approach was taken to avoid later criticism of the vice president for being too harsh.

In the run-up yesterday to the Cheney-Edwards debate, Mr. Kerry and the Bush campaign kept up a back-and-forth skirmish over Iraq policy, with the Democrat charging that President Bush has been too stubborn to admit having made serious errors. Campaigning in Iowa, a swing state Vice President Gore won narrowly four years ago, Mr. Kerry dismissed the president’s charge, made the day before, that his policies would be dangerous for world peace. The Massachusetts senator accused Mr. Bush of engaging in a scare tactic.

The senator was provided his sharpest attack line by the former American administrator in Iraq, Paul Bremer. Pouncing on an acknowledgment by Mr. Bremer that America had “paid a big price” for insufficient troop levels after ousting Mr. Hussein, Mr. Kerry said voters would have to decide whether Mr. Bush was “constitutionally incapable of acknowledging the truth” or was “just so stubborn.”

The Kerry attack was left unanswered by Mr. Bush, who was in the White House working on a major speech about Iraq to deliver in Pennsylvania today. Campaign aides defended the president, arguing that Mr. Bush consulted field commanders rather than his Iraq administrator when it came to troop requirements.

Both campaigns claimed victory after the vice presidential debate. Senator Lieberman said Mr. Edwards had done well and “built up the momentum from John Kerry’s good performance in the debate with the president last Thursday.” Mr. Lieberman said that although vice presidential debates normally don’t have much impact on elections, this time it could. “It is a close election and everything counts.”

A former GOP senator, Alan Simpson, gave the nod to Mr. Cheney, as did some TV pundits. “It was a case of Mr. Steady versus Nice and Excitable. Edwards always tried to get the last lick in, just like a trial lawyer.”

Attention will now turn to the second debate between Messrs. Bush and Kerry this Friday.