Mitt Romney and the Republican Party have begun a late push to raise tens of millions of dollars in the closing weeks of the election, cash that will finance a last-minute barrage of advertising that Mr. Romney’s aides believe is critical to beating President Obama.

In an e-mail to top donors and fund-raisers on Monday afternoon, Mr. Romney’s campaign said that it had raised $170 million in September, almost as much as the near-record $181 million raised by Mr. Obama, but the campaign added that it needed to bring in even more money in October to capitalize on Mr. Romney’s surge in polls in swing states like Florida and Ohio.

The announcement opened a three-day retreat for donors at New York’s Waldorf-Astoria hotel, where the campaign is seeking to tap into a burst of enthusiasm among formerly jittery donors — who were energized by Mr. Romney’s strong first debate performance — to recruit new donors and persuade old ones to give the maximum allowed by law. Big donors will also spend part of the retreat working the phones in a miniature call-athon intended to wring out as many last-minute dollars as possible.

Mr. Romney had considered making a quick appearance at the retreat, but ultimately decided to stay in Boston to prepare for Tuesday night’s debate on Long Island. Quietly, his donors had been sending the message to his finance team: They would love to see Mr. Romney, but three weeks from Election Day, they felt his time was probably better spent practicing for his face-off with Mr. Obama or hitting the campaign trail.

The Romney campaign’s broad effort will be an experiment in last-minute high-dollar fund-raising by a presidential campaign, one made necessary by Mr. Romney’s decision to forgo public financing and the threat posed by the millions of small donors supporting Mr. Obama, who similarly opted out of public financing.

Those small donors have flooded Mr. Obama’s campaign with a steady stream of money with little investment of the president’s time and energy, allowing him to focus more heavily on retail campaigning in recent weeks. While Mr. Romney’s fund-raising has kept roughly on pace with Mr. Obama’s since the beginning of the summer, his dollar totals lean more heavily on large checks to the Republican National Committee, which must pay higher rates for political advertising and is allowed to spend only a limited amount on ads coordinated with Mr. Romney’s campaign.

With less ready cash in its own accounts, Mr. Romney’s campaign was forced to restrain its spending during the summer advertising war. The Romney campaign is eager to strike back now, in a last-ditch effort to sway undecided voters.

“We are pleased to announce that Romney Victory raised $170 million in the month of September,” Spencer Zwick, the campaign’s national finance chairman, said in the e-mail. “This is truly an incredible testament to this group’s commitment and hard work and represents the largest amount of money we have raised to date in any given month of the campaign.”

The three-day retreat in New York is a follow-up to the star-studded “Republicanpalooza” the campaign held in June in Park City, Utah.

In New York, the $50,000 entrance fee, which most of the donors long ago raised, got Mr. Romney’s “Founding Partners and Members” and “Stars and Stripes” club members into a dinner Monday night at the Intrepid Sea, Air and Space Museum, as well as a packed day of panels on Tuesday.

Headliners at the Intrepid dinner include Representative Paul D. Ryan, Mr. Romney’s running mate; former Mayor Rudolph W. Guiliani of New York; Reince Preibus, the Republican National Committee chairman; Donald Trump, and Mr. Zwick.

Mr. Ryan also hosted his own cocktail and photo reception Monday afternoon at the Hilton New York — $1,000 per person and $5,000 for a photo. On Monday morning, one prominent hedge fund manager serving as a co-chairman for the event e-mailed a blast solicitation to his contacts. He pointed them toward an article on Politifact about Mr. Romney helping a colleague of from Bain Capital help locate his missing teenage daughter. The article, wrote the hedge fund manager, helps “demonstrates the kind of leader Mitt Romney is.”

“If you believe in capitalism over socialism and that our country’s fiscal debt crisis is the most important issue facing us today, I ask that you strongly consider donating to his campaign and asking your friends to do so as well,” the financier wrote.

The nearly 200 co-chairmen and -women of the Ryan event include some of the more public supporters of Mr. Romney, including the New York Jets owner Woody Johnson and prominent hedge fund executives including Daniel S. Loeb and Anthony Scaramucci.

Panels at the Waldorf include sessions like “Campaign and Strategy Briefing,” featuring Rich Beeson, the campaign’s political director; Ed Gillespie and Beth Myers, senior strategists for the campaign; Neil Newhouse, Mr. Romney’s pollster; and Mr. Priebus.

The session “Issues Facing America — Jobs,” will include remarks by Carlos Gutierrez, a former secretary of commerce; Harold Hamm, an oil magnate and energy adviser to Mr. Romney; Jimmy John Liautaud, chairman of the Jimmy John’s restaurant chain; Scott G. McNealy, co-founder of Sun Microsystems; and Charles Schwab, chief executive of the Charles Schwab Corporation.

Mr. Zwick will address the final session, “Make the Difference,” in what is probably a final pitch to donors in the end stretch.