The increasingly rough-and-tumble presidential campaign will descend in force on New York today as both President Bush and Senator Kerry of Massachusetts make visits to the city.

Senator Kerry is planning three local events, including a morning speech at New York University that aides are billing as a major policy address on Iraq.

Mr. Bush is scheduled to attend a fund-raising event tonight in Manhattan before speaking tomorrow at the opening of the United Nations General Assembly.

The candidates’ appearances in New York come as Iraq and the war on terror have vaulted to center stage in the presidential race. Over the weekend, the two camps hurled insults at each other, with Democrats suggesting that Mr. Bush is indifferent to the turmoil in Iraq and Republicans painting Mr. Kerry’s statements on the subject as incoherent.

Speaker of the House Hastert stoked the partisan fires further on Saturday night when he said he believes Al Qaeda would like to see Mr. Kerry win in November.

“I don’t have data or intelligence to tell me one thing or another, but I would think they would be more apt to go for somebody who would file a lawsuit with the World Court or something rather than respond with troops,” Mr. Hastert said at a news conference before a Republican fund-raising dinner in DeKalb, Ill.

Pressed on whether he was suggesting that Al Qaeda would be better off with Mr. Kerry in office, Mr. Hastert said, “It’s my opinion. Yes.”

The Democrats’ vice presidential candidate, Senator Edwards of North Carolina, expressed outrage at the charge.

“Denny Hastert, the speaker of the House, has joined the fear-mongering choir,” Mr. Edwards said as he campaigned in Pennsylvania yesterday. “When John Kerry is president of the United States, we will find Al Qaeda and crush them before they can do damage to the American people.”

Democrats signaled that they plan to spend this week – and perhaps the rest of the campaign – relentlessly attacking Mr. Bush’s Iraq policy.

The Democratic National Committee has invited mothers of American military personnel serving in Iraq to denounce Mr. Bush at a press conference in Washington today.

“George Bush is like an ostrich with his head in the sand. He can’t face reality,” said the party’s national chairman, Terence McAuliffe. “We have to talk realistically about what’s happening. Tell the parents of the 1,000 soldiers that have been killed in Iraq.”

During a conference call with reporters, Mr. McAuliffe was asked if some voters might see the Democrats’ message as undermining the resolve of American forces.

“Unfortunately for America, it is a pessimistic situation in Iraq, but this is George Bush’s war,” Mr. McAuliffe said. “It’s only getting worse … George Bush thought they would be throwing rose petals at them as they marched down the street. They’re not. They’re killing our troops.”

The chairman of the Republican Party, Edward Gillespie, said it sounded like the Democrats were ready to abandon the fight against the terrorists in Iraq.

“We’re going to have victory in Iraq. That is critically important for our national security interests, that we not engaged in a policy of retreat and defeat, which is what you increasingly hear out of the Kerry camp,” Mr. Gillespie told CNN yesterday.

The GOP leader said Mr. Kerry had failed to offer a viable alternative to Mr. Bush’s policy.

“Senator Kerry has moved beyond inconsistency, when it comes to Iraq, to utter incoherence,” Mr. Gillespie said. “When you try to figure out what his position is, sometimes it’s painful. It’s like pig Latin, trying to figure out what he’s trying to say.”

The decision by the Kerry camp to focus squarely on Iraq appeared to be a rejection of advice President Clinton gave Mr. Kerry a couple of weeks ago. Mr. Clinton reportedly told Mr. Kerry to focus more on job creation and health care.

Curiously, the decision to turn more attention to Iraq was made just as a gaggle of former Clinton aides joined the Kerry campaign.

The shift towards foreign policy was also driven, to some extent, by necessity. Mr. Bush’s schedule at the United Nations this week is peppered with high-profile meetings with foreign leaders. And, on Thursday, the interim prime minister of Iraq, Ayad Allawi, is scheduled to make a historic visit to the White House.

Mr. Kerry’s campaign aides declined to discuss his Iraq speech in detail yesterday. A top foreign policy adviser to Mr. Kerry, Richard Holbrooke, suggested that the thrust of Mr. Kerry’s critique will be that America is trying to do too much in Iraq with too few troops and too little help from other countries.

“We have a classic mismatch between resources and mission,” Mr. Holbrooke said on CBS’s Face the Nation. “The current course within the current resources is not achievable. If you want to achieve that course, you’re going to have talk about additional forces, and they’re not going to come from our allies, or you’re going to have to look for a way to get the political settlement,” the former diplomat said.

During a press conference in London yesterday, the Iraqi leader, Mr. Allawi, said that the recent surge in unrest in his country will not lead to postponement of the planned elections.

“We definitely are going to stick to the timetable of elections in January next year,” Mr. Allawi said. He said the surge in bombings, kidnappings, and street fighting that have claimed some 300 lives in the past week only serves to underscore the need to move forward.

“January next, I think, is going to be a major blow to terrorists and insurgents. Once we go through the democratic process, once we achieve and progress toward democracy, the terrorists will be defeated,” Mr. Allawi said.

Mr. Holbrooke said the Iraqi official’s statements ignored reality.

“Prime Minister Allawi’s comments remind me of Groucho Marx’s great line, ‘Who do you believe, me or your own two eyes?'” Mr. Holbrooke said. He said the situation in Iraq at present is worse than the one American troops faced in Vietnam three decades ago.

“We could walk around the cities of Vietnam freely day and night,” he said. In Iraq, Mr. Holbrooke said, “They’re getting mortared. In the Green Zone, they wear helmets and flak jackets in their inner, inner sanctum. The situation is not as Allawi portrayed it.”

In an interview with the Manchester Union Leader on Saturday, Mr. Bush said he continues to be hopeful about Iraq.

“I’m pleased with the progress. It’s hard, don’t get me wrong,” Mr. Bush said. “We’re on the right path, and I intend to keep us there.”

A Republican senator, however, said yesterday that the administration needs “some re-calibration of policy” on Iraq.

“I don’t think we’re winning,” Mr. Hagel told CBS. “To say, ‘Well, we just must stay the course and any of you who are questioning are just handwringers,” is not very responsible. The fact is we’re in trouble. We’re in deep trouble in Iraq.”

Mr. Kerry’s Iraq speech this morning at NYU’s Kimmel Center will be open to the school’s students and faculty on a first-come, first-served basis, an NYU official said yesterday.

In the afternoon, Mr. Kerry is scheduled to speak at a luncheon at Lincoln Center sponsored by Redbook magazine. The annual event, known as the “Mothers and Shakers Awards,” salutes influential women. Mr. Kerry will be accompanied throughout the day by his wife, Teresa Heinz Kerry, a campaign aide said.

Mr. Kerry is also expected to tape an interview with David Letterman before attending an evening fund-raising reception at the Hilton New York.

At roughly the same time, Mr. Bush is scheduled to be raising money a few blocks away at the Sheraton New York. Both Mayor Bloomberg and Mayor Giuliani are listed as honorary co-chairs of tonight’s fund-raiser. The minimum donation is $2,000 per person.

Mr. Bloomberg is not expected to attend, but Mr. Giuliani plans to be on hand.