DES MOINES, Iowa (Reuters) - Howard Dean's high-flying campaign for the Democratic presidential nomination suffered a body blow in the Iowa caucuses on Monday, but the former Vermont governor vowed to fight on, declaring, "We will not give up."

His voice raspy, Dean, who finished a stunning third in the first contest of the 2004 White House race after once being one of the favorites in Iowa, shouted to supporters, "We are not only going to New Hampshire," then hoarsely listed at least a dozen states that hold contests in the next few months.

"We will not quit now or ever!" he told about 1,000 supporters. "We have just begun to fight."

Even before Iowans finished publicly stating their preferences U.S. television networks projected Massachusetts Sen. John Kerry and Sen. John Edwards of North Carolina had beaten Dean.

"I would have loved to have come in first tonight ... but we got our ticket punched to New Hampshire," Dean said. That state holds its first-in-the-nation primary on Jan. 27.

With 18 percent of the vote, Dean finished 20 points behind the winner, Kerry. Edwards scored a surprise second-place finish with 32 percent in nearly complete returns.

Missouri Rep. Richard Gephardt was fourth with 11 percent and gave up his race for the U.S. presidency. That left seven Democrats vying for the right to challenge President Bush in the Nov. 2 presidential election.

Dean was taking a midnight flight to Portsmouth, New Hampshire, where he planned to hold a predawn rally after appearing before supporters in a Des Moines ballroom.

He holds a slim lead over Kerry and retired Gen. Wesley Clark in polls for the New Hampshire primary. Dean has led the field in national surveys of Democratic voters.

Dean lost in Iowa despite high-powered endorsements from former Vice President Al Gore, former New Jersey Sen. Bill Bradley and Iowa's most popular politician, Sen. Tom Harkin. On Sunday, Dean received a strong signal of support from former President Jimmy Carter but not an official endorsement.

"You get three tickets out of Iowa," said Dean's campaign manager, Joe Trippi. "We got one of them. It's not the one I would have wanted but I'll take it."

'PIN CUSHION'

Dean, whose clever use of the Internet to raise $40 million and attract new supporters, helped propel him to the top of the polls late last year, complained he had been a "pin cushion" for his rivals and the media because of his front-runner status.

His bluntness and propensity to speak his mind occasionally tripped him up, allowing opponents to paint him as gaffe-prone and not ready for the White House.

"That was the problem, we were way ahead, and when you're way ahead people decide you're the target, and we were pretty much the target of everybody for a long time, and it was hard to sustain that," Dean said on CNN's "Larry King Live."

But Iowans apparently rejected the outsider's hard-edged antiwar rhetoric and his anti-establishment message in favor of two Washington insiders.

The formidable ground organization Dean built up over two years of visiting Iowa failed to carry the day. More than 3,000 Dean volunteers flooded the state, knocking on doors and making telephone calls in what the campaign dubbed "The Perfect Storm."