With the Iraq war a dominant issue in America's mid-term congressional elections on November 7, Kerry's comment has been seen as a gaffe that has given Republicans a boost in the run-up to the polls.
While campaigning in California, Kerry told a college crowd on Monday: "You know, education, if you make the most of it, you study hard, you do your homework and you make an effort to be smart, you can do well. If you don't, you get stuck in Iraq."
George Bush, the US president, quickly seized on the controversy and demanded that Kerry should apologise.
Bush said at a campaign rally in Georgia where the crowd booed at Kerry's quote: "The senator's suggestion that the men and women of our military are somehow uneducated is insulting and it is shameful.
"The members of the United States military are plenty smart and they are plenty brave and the senator from Massachusetts owes them an apology."
Senator John McCain, an Arizona Republican and a fellow Vietnam vet who has had an amicable relationship with Kerry said the senator "owes an apology to the many thousands of Americans serving in Iraq, who answered their country's call because they are patriots and not because of any deficiencies in their education".
Other Republican politicians and conservative talk-show hosts made similar calls.
Paul Morin, national commander of the 2.7 million-member American Legion, the nation's biggest veterans' organisation, expressed outrage.
White House spokesman Tony Snow had called the comments "an absolute insult".
Bush said Kerry should apologise
for his comment on US soldiers
Kerry, who served in the Navy in the Vietnam War and unsuccessfully challenged Bush in the 2004 presidential election, has refused to apologise and said his remark was a "botched joke" aimed at the president and not US soldiers.
The Massachusetts Democrat said at a news conference in Seattle: "The people who owe our troops an apology are George Bush and (Vice President) Dick Cheney who misled America into war."
Staff at his office later said the Massachusetts Democrat had misread his prepared remarks that included the words "Just ask President Bush", which he omitted.
War in Iraq
US Senate candidate Ben Cardin, a Maryland Democrat, said he was sorry about Kerry's choice of words but insisted that the main issue was the war in Iraq.
"I think what the Republicans are going to try to do is use this as a distraction. But the voters are smarter than that. They know things are not going well. And they know the president does not have a plan to get us out of Iraq," he said on CNN.
A Democratic congressional candidate in a close race in Iowa has cancelled a campaign event with Kerry, saying the senator's comments were inappropriate.
Kerry has also cancelled an appearance for a Democratic candidate in Minnesota.
The two main parties are searching for any edge amid indications that the Democrats could take back the House of Representatives and possibly win control of the Senate in next week's mid-term legislative elections.