WASHINGTON – As Florida moved yesterday in opinion polls from a Bush-leaning state to a tossup, Senator Kerry launched a fierce counterattack against the president. The Democrat rebutted Republican accusations that he’s ill-equipped to be commander in chief and argued that Social Security is on the line on Election Day.

The Kerry campaign rolled out two new TV spots that it hopes will bolster the Massachusetts senator’s credentials on national security and blunt the impact of Republican attacks. According to a Kerry spokesman, Michael Mc-Curry, the ads bemoaning “the mess in Iraq created by George Bush” are part of an end-game effort to reduce Mr. Bush’s lead in opinion polls when it comes to issues of national security and the war on terror.

Campaigning in Florida, where a Survey USA poll suggests Mr. Kerry has clawed out a one-point lead, and later in Pennsylvania, Mr. Kerry scored the president for his tax cuts and warned that the incumbent wants to mount an “all-out assault” on Social Security.

“On November 2, Social Security is on the ballot,” Mr. Kerry said. He argued that the voters are faced with a “choice between one candidate who will save Social Security and another who will undermine it.”

The Democrat rejected the president’s accusations that he stands for “protest and defeatism” in Iraq, telling supporters he will bring a fresh start and new credibility to the war effort. “Have no doubt about it, we will hunt down, capture, or kill the terrorists wherever they are in the world,” Mr. Kerry said.

His running mate, Senator Edwards, made the same arguments in New Hampshire and in Ohio, where polls give the Democratic ticket a slim lead. The vice-presidential nominee accused Mr. Bush of failing the United States and the world in Iraq. He cited unsecured nuclear weapons abroad and unprotected ports at home as evidence of presidential ineptitude. The North Carolina senator said: “He’s created something that didn’t exist before the war in Iraq – he’s created a haven for terrorists. … This is not leadership, this is incompetence.”

Touring the must-win state of Florida with his brother, the state’s governor, Jeb Bush, the president stepped up his offensive, telling supporters that his Democratic challenger could not be trusted to wage the global war on terrorism. The president charged that Mr. Kerry had voted against crucial weapons systems and he mocked the Democrat for saying America should use military force only if it passes a “global test.”

“My opponent is not prepared and equipped to be the commander in chief,” the president said. In Ohio, Vice President Cheney evoked the possibility of terrorists’ bombing American cities with nuclear weapons and questioned whether Mr. Kerry could combat such a threat.

On campaign stops along the Interstate 4 corridor, which stretches across Florida’s midsection from Tampa Bay through Orlando to Daytona Beach and has a high concentration of swing voters, the president took pains to answer Mr. Kerry’s charge that his administration was at fault for shortages of flu vaccine.

“I know there are some here who are worried about the flu season,” Mr. Bush said. “I want to assure them that our government is doing everything possible to help older Americans and children get their shots despite the major manufacturing defect that caused this problem.”

On Monday, while stumping in Florida, Mr. Kerry played up the lack of vaccine. The Democrat said: “If you can’t get flu vaccines to Americans, how are you going to protect them against bioterrorism? If you can’t get flu vaccines to Americans, what kind of health care program are you running?” Mr. Kerry said the Bush administration failed to heed warnings from British authorities about the curtailing of vaccine shipments to America because of a questionable manufacturing process.

The president assured his campaign audiences that there are millions of vaccine doses on hand for vulnerable Americans. “Millions more will be shipped in the coming weeks,” he said. “We’re stockpiling more than 4 million doses of flu vaccine for children.”

Mr. Bush sought also to rebut Mr. Kerry’s claim that a Republican victory would create “great potential of a draft.” He pledged not to reinstate a military draft if re-elected, emphasizing, “We’ll keep the all-volunteer army. I repeat. The all-volunteer army will remain an all-volunteer army.”

Special-interest groups backing Mr. Kerry have been feeding rumors of a draft in a second Bush term. MoveOn-StudentAction.org has mounted a nationwide college “Feel a Draft?” campaign. Both the Kerry and Bush camps are wooing younger voters, and Republicans are keen to quash any suggestion that a draft could be introduced.

With the race still in flux, the campaigns are focusing their efforts increasingly on a handful of battleground states, including Florida, Pennsylvania, and Ohio, which saw the bulk of yesterday’s political action by the party tickets. The Sunshine State, the Keystone State and the Buckeye State account for a fourth – 68 – of the 270 electoral votes needed to win.

According to an NBC News analysis, Mr. Bush is leading in states with 217 electoral votes, while his rival is leading in states with 200 votes. The remaining states and their 121 votes are too close to call.

The manager of the Bush campaign, Matthew Dowd, said the president has picked up some momentum since the conclusion of the series of debates with Mr. Kerry. In an online note on the state of the race, Mr. Dowd wrote: “The president is doing increasingly well among voters deemed a part of the key swing group: the president is winning independent voters, he is doing better among women voters than 2000,and we have the opportunity to achieve historic gains among minority voters.”

Mr. Dowd acknowledged that Mr. Kerry had managed to energize the Democratic base during the debates, closing the race to dead even. But he said Mr. Bush is on the upswing and has now returned the race virtually to where it was before the debates, when the president enjoyed a lead of 5 percentage points, thanks to key issues of terrorism and Iraq.

Bush campaign aides are also pleased with a poll released yesterday that suggests the president has doubled his support among black voters since the last election. The poll by the Joint Center for Political and Economic Studies, a Washington-based research group, found also that Mr. Kerry’s backing among blacks is down slightly from the support Al Gore won in 2000.

Despite that, the Democratic nominee enjoys a nearly 4-1 edge over Mr. Bush among blacks, with the poll giving the Massachusetts senator 69% and Mr. Bush 18%. But even a slight erosion of black support for the Democratic nominee could prove crucial, and he needs a large turnout among blacks to win battleground states.

Mr. McCurry, the Kerry campaign adviser, said the Democratic ticket was well-positioned for the final fortnight of the race. He told reporters on Mr. Kerry’s campaign plane that if the Democrats are able to “defeat … or neutralize” the GOP edge on the war on terror, then “we’ll be in a very strong position in the closing days of the campaign.”

While both campaigns expressed confidence about their chances of success, Democratic and Republican officials admitted they are haunted about the balloting intentions of new voters, who are being brought in by aggressive registration campaigns. The Democrats appear to be gaining the upper hand in the important side-battle to sign up new voters.

An Associated Press analysis has found that the Democrats have registered more new voters than Republicans in Arizona, Iowa, New Mexico, Nevada, and New Hampshire. In Florida the GOP has a slight edge.

Party officials said new voters may be the November surprise and worry that opinion polls may not be reflecting accurately how many of them will vote and for whom.