Cheney accused Kerry of making a "habit of indecision," saying he does not understand the world and cannot be trusted to protect the nation. President Bush, he said, has led with strength and conviction.
In a speech accepting his party's nomination for a second term, Cheney paid brief homage to Kerry's service in Vietnam and then said he has been wrong on foreign policy in the three decades since.
"Even in this post-9/11 period, Senator Kerry doesn't appear to understand how the world has changed," Cheney said. "A senator can be wrong for 20 years, without consequence to the nation. But a president always casts the deciding vote."
Cheney followed Sen. Zell Miller to the podium. The Georgia Democrat delivered a searing indictment of his own party and its presidential nominee, saying that on issues of freedom and security, "John Kerry has been more wrong, more weak and more wobbly than any other national figure."
Speaking as the convention keynoter 12 years after he was keynote speaker for the Democrats in the same Madison Square Garden, Miller enthusiastically endorsed Republican President Bush.
"I have knocked on the door of this man's soul and found someone home, a God-fearing man with a good heart and a spine of tempered steel," Miller said.
Mr. Bush, who arrived in New York and collected the endorsement of the union representing the city's 8,600 firefighters, some of whom risked their lives on Sept. 11, 2001, is scheduled to accept his party's nomination Thursday night.
White House communications director Dan Bartlett told CBS' Early Show co-anchor Harry Smith the president will explain in his speech why it is so critically important at this juncture in our history that we move forward.
"President Bush in the time of war has made some very difficult decisions, and he will speak from the podium tonight and talk to our soldiers and talk to the world about why we're doing what we're doing,"
The Cheney and Miller speeches followed a tribute to former President Ronald Reagan, who died earlier this year.
Cheney performed the traditional vice president's role of praising the man at the top of the ticket while denigrating the leader of the political opposition.
"What we heard from the Republicans in that hall last night, was an enormous amount of anger and very little … discussion about what they're going to do about healthcare, what they're going to do about jobs, what they plan to do about this mess in Iraq." Democratic Vice Presidential nominee John Edwards told CBS' Early Show co-anchor Hannah Storm. "We offered something very different in our convention, which was hope and optimism and a real plan to deal with all of these serious things that the American people face."
Dropping some of his more strident rhetoric about why the administration went to war, Cheney said the United States "dealt with a gathering threat" from Saddam Hussein and restored freedom to the Iraqi people.
The vice president made no mention of al Qaeda leader Osama bin Laden, still at large and defended the Bush record on domestic issues education, taxes, the economy and health care.
Kerry was in Nashville, Tenn., on Wednesday speaking to the same American Legion gathering that Mr. Bush addressed the day before. Noting that the president said earlier in the week that the terror war could not be won, Kerry said, "With the right policies, this is a war we can win."
In a television interview that aired Monday, Mr. Bush said the terror war couldn't be won. He amended the comment in his speech to the American Legion, saying it could be won.
Kerry's appearance broke a tradition in which presidential candidates have refrained from campaigning during the other party's convention. He used the occasion to again criticize Mr. Bush's Iraq policy.
"I would never have gone to war without a plan to win the peace," Kerry said.
CBS News Correspondent Byron Pitts reports Joe Lockhart, President Bill Clinton's former press secretary, has been brought in, along with other Clinton veterans, to sharpen Kerry's public image and to apply the old Clinton playbook: When attacked, attack back even harder.
There was some evidence of that strategy Wednesday.
"When it comes to Iraq, it's not that I would have done one thing differently, I would have done almost everything differently," Kerry told an audience in Nashville.
As Wednesday night's program got underway, Republican delegates wrapped up the traditional roll call of the states, making President Bush their unanimous choice to lead their ticket in November.
Outside the convention hall,as thousands of people waving pink slips formed a line three miles long to protest the Bush administration's economic policies.
A small group of AIDS activists managed to penetrate Madison Square Garden itself, although the convention was not in session at the time. They blew whistles and chanted, "Bush kills," at a morning session of GOP youth before being hustled from the floor.
Police said convention-related arrests over the past week now totaled more than 1,700.
Cheney, 63, who served in President George H.W. Bush's administration as defense secretary, has seen his approval ratings plummet amid persistent questions about his role in promoting the Iraq war and in handling the Sept. 11 terror attacks.
But Mr. Bush has stuck fast by him, even as a new CNN/USA Today/Gallop poll conducted last week showed that 52 percent of those surveyed said they would vote for Democrat John Edwards for vice president over Cheney, if they could select the vice president separately.
Asked whether Cheney had given Mr. Bush good advice or bad advice over the past four years, 41 percent answered "good advice," 39 percent answered "bad advice" and 17 percent said they were unsure.