Buoyed by signs that an embattled President Bush has gained ground in the past two weeks, Republicans began gathering Saturday for a national convention designed to highlight Bush's leadership on terrorism, sketch out themes for a second term and continue a months-long effort to discredit Democratic nominee John F. Kerry.

Republican strategists said they want to use the convention to begin to neutralize public dissatisfaction over Iraq and the economy, which has put Bush's reelection at risk, by shifting voters' focus from their qualms about the state of the country, which Kerry has exploited, to a choice between a president who will portray himself as steady and consistent vs. a challenger whom GOP speakers plan to hammer as the opposite.

Republican delegates are arriving in the city that felt the worst of the devastation from the attacks of Sept. 11, 2001, amid extraordinary security, particularly in the blocks surrounding Madison Square Garden, where Bush will accept his party's nomination for a second term on Thursday. Convention officials were braced for large and potentially disruptive demonstrations and protests, beginning Sunday.

As New York officials finished their preparations, Bush and Kerry spent Saturday on the campaign trail. Bush held a rally in Ohio, where he previewed his Thursday night speech by describing his foreign and domestic policies as transformational, while Kerry campaigned in Washington before returning to his home on Nantucket island for a few days of rest.

The convention will open Monday with the GOP encouraged by half a dozen national polls released in the past four days. Numbers show the presidential race still essentially in a dead heat, but with Kerry having given back some of the gains from his convention in Boston last month and Bush narrowly ahead rather than narrowly behind.

Republican strategists attribute the shift in part to the damage inflicted on Kerry by the controversy over his Vietnam War service raised by the group Swift Boat Veterans for Truth. And some Bush advisers say Kerry was hurt by his remark that, knowing what he does now, he still would have voted to authorize the president go to war in Iraq.

"I like the president's position a lot better going into this convention than I did five weeks ago going into the Democratic convention," Republican pollster Linda DiVall said.

But the sense of relief that Bush's condition looks better than expected did little to obscure deeper concerns among Republicans about the overall race that still tilts against the president and about the importance of using the convention to move the contest more decisively in his direction.

"You can't frame the election about how people feel today -- you've got to frame the election on who has better ideas for the future," said a GOP strategist who asked not to be identified in order to speak more freely about the challenges facing Bush.

The president begins his convention weaker than recent presidents who won reelection but stronger than the last two who lost reelection bids, including his father 12 years ago. Although voters see Bush as a strong leader and as likable, he faces an electorate eager for a change in the direction of the country, disappointed in the way he has handled Iraq and the economy.

A new NBC News-Wall Street Journal poll found that voters strongly side with positions or statements Kerry has articulated about the economy, withdrawing troops from Iraq and whether the United States should be willing to act unilaterally or in conjunction with other nations on foreign policy.

Bush's challenge this week, say strategists in both parties and outside analysts, will be to convince wavering voters, particularly in battleground states, that he represents a better -- and safer -- bet for the next four years than his challenger, whatever personal feelings those voters have about Bush's first term.

"One thing he's got to do -- and it is remarkable that he has to do this at this point -- is that he's got to put together a reasonable defense of his own record," said William Mayer, a political scientist at Northeastern University. "But I would also be going after Kerry. . . . I would sure spend a lot of time going after him."

Tom Rath, a GOP committee member from New Hampshire, predicted the Bush team would do that. "I will guarantee you that John Kerry's Senate record will be discussed more here than it was in Boston," he said. "They're going to go after that."

Bush advisers believe that in focusing heavily on his war record, Kerry missed an opportunity to talk more about his political record and agenda. "The Boston convention was about a biography that stopped 20 years ago -- this convention will be about real solutions to real problems that people face today," said Ken Mehlman, Bush's campaign manager.

Rath said Bush's advisers also plan to reshape what has been a politically troublesome and divisive debate over Iraq into a far broader discussion about which candidate can wage a more effective war on terrorism, an issue on which Bush continues to hold the advantage.

That will start Monday night with speeches by former New York mayor Rudolph W. Giuliani and Arizona Sen. John McCain, two men who Bush advisers say have the credentials and national credibility to make that case to undecided voters. "The Democrats want to discuss the war on terror [as if it started] about six months ago," Rath said. The GOP speakers, he said, are "going to bring it back to 9/11."

A top Bush adviser, asking not to be identified in order to talk about strategy, said the president and others will challenge Kerry on his contention that only he would work cooperatively with other nations. "Do you think this campaign is going to be about one guy who says I'm going to go it alone and one guy who says I can bring other countries together? No," the adviser said. Instead, he said, Bush will cast the choice as one between someone who has put different coalitions together "and another who says we've got to make France and Germany come with us."

GOP officials said Bush will describe his first-term accomplishments and his ambitions for a second term as an effort to transform the federal government and the world, focusing on the progress toward democracy in Afghanistan, which is preparing for elections, and that he seeks for Iraq. He also plans to describe his No Child Left Behind education act, the addition of prescription drug benefits to Medicare, the creation of the Homeland Security Department and his goal of partially privatizing Social Security as challenging the status quo.

Bush advisers said not to expect big new initiatives or detailed proposals. Instead, they suggest the president will use a broad brush while raising the stakes of the choice in November. He will offer a vigorous defense of his belief that his aggressive approach to terrorism will keep the country more secure than Kerry's approach. Said one adviser: "There is a big choice in this election, about foreign policy, about the war on terror and about the personal characteristics about these individuals."

Kerry advisers say Bush will have trouble achieving his goals this week, in part because many of the voters he will be trying to reach dislike the policies he has pursued. "He needs to change the public perception of his presidency and the mood about where the country is," said Kerry strategist Tad Devine. "He's got to somehow navigate an electorate which is heavily weighted against him when it comes to the policy prescriptions he's laid out."

But with a little over two months before the election, Bush has little time in which to make that case, and while his convention offers his best opportunity to date to do so, some analysts say he has failed to take advantage of the powers of the presidency to do so already.

"I've long felt that the Bush White House, in particular, has not done a very good job of communicating the president's message," Mayer said. "To a greater extent than any presidency I can think of, they've abdicated the bully pulpit. They've not made any attempt to communicate a clear message, particularly about events in Iraq."

Given the highly polarized electorate, outside analysts say they do not expect Bush to get a significant bounce in the polls, pointing to the relatively small gains in the head-to-head matchup Kerry got from his convention. But the mood of the president's advisers has brightened as they arrive for their convention, believing they have weathered a potentially difficult month.

"The sense here is that we're going into the convention a bit stronger than we thought," a senior administration official said. "We're kind of going in where we thought we would come out [of New York]. But there's no euphoria. This is still a dead-even race, and it probably will stay that way right to the end."

Staff writer Mike Allen, traveling with Bush, contributed to this report.

The blocks surrounding Madison Square Garden will be under tight watch all week.