NEW YORK (CNN/Money) - The Dow Jones industrial average made a fighting comeback with a triple-digit rally Tuesday, posting its strongest gain in six weeks at the start of a new month and new quarter.

The 30-share Dow, the world's most widely watched stock average, jumped 347 points, with much of the gains coming late in the session, after news that Iraq had agreed to allow the return of U.N. weapons inspectors; an advance team is due in Baghdad in about two weeks.

Martin Mauro, senior economist at Merrill Lynch, and Sam Stovall, senior investment strategist at Standard and Poor's, take a look ahead at the final three months of 2002. Play video (QuickTime, Real or Windows Media)

The development may dampen the prospect of war, and it helped push a weak manufacturing report out of the picture. The chance of a war with Iraq has unnerved investors in recent months, contributing to one of the worst market selloffs in recent memory.

"The Iraq news definitely was a positive. This morning, people were fearful of the ISM data, which came mostly in line. So stocks tracked higher on these developments," said Tony Dwyer, market strategist with Kirlin Securities.

But some traders curbed their enthusiasm over the day's performance.

"I think people are waiting for the dust to settle," Tim Smalls, equity trader with SG Cowen, told CNNfn's Street Sweep. "We've had so many issues to deal with over the past year that this one day and a great start to the quarter -- it gets us off on a good note. But I wouldn't necessarily put a tremendous amount of stock into it as changing people's psyche on the markets."

The market rally came a day after the major stock indexes closed the book on both an abysmal September and the worst third quarter since the market crash of 1987.

The Dow Jones industrial average (up 346.86 to 7938.79, Charts) jumped 4.6 percent -- its third-best percentage gain this year -- to close within striking distance of 8,000. The Nasdaq composite (up 41.66 to 1213.72, Charts) gained 3.6 percent, and the Standard & Poor's 500 (up 32.63 to 847.91, Charts) rose 4 percent -- its fourth-biggest percentage gain for the year.

The Nasdaq overcame early losses after an upgrade of Dell Computer and a "lucky" mistake by Sun Microsystems.

Market watchers said a combination of hope and anxiety on the part of investors provided some early support to the market despite some troubling news on the economy.

"The Dow [showed] some resolve. I think it [had] to do with a key report on employment that indicates the jobs picture may be firming up," said Charles Payne, CEO and chief market strategist with Wall Street Strategies.

Employment research firm Challenger Gray & Christmas said job cuts announced at U.S. firms sank 41 percent to a 22-month low in September. That may bode well for Friday's September jobs report, Payne said. Economists are forecasting that unemployment ticked back up to 5.9 percent last month from 5.7 percent in August.

Other economic news was less encouraging to investors. Manufacturing shrank last month for the first time since January, while construction activity fell in August.

Among the market movers, Dell (DELL: up $1.13 to $24.64, Research, Estimates) took off after Banc of America late Monday upgraded the stock to "buy," citing stronger conviction of sustainable growth, including the PC maker's recent entry into new market segments.

After the market closed, the No. 2 personal computer maker raised its sales target and said it expects profits at the high end of its prior forecasts for the latest quarter, sending its stock higher in after-hours trading.

Sun Microsystems (SUNW: up $0.17 to $2.76, Research, Estimates), the leading supplier of Unix servers, late Monday restated its fourth-quarter earnings higher, citing lower costs than previously calculated. But Goldman Sachs dented the positive news by widening its loss estimate for the company's September quarter, saying more job cuts could be coming.

Shares of tech bellwether IBM (IBM: up $2.86 to $61.17, Research, Estimates) got a boost after Britain's top health and beauty retailer Boots announced a $1.1 billion 10-year deal with IBM to manage its computer infrastructure and telecommunications systems.

But it was not all smooth sailing for techs as some other prominent companies got hit by analysts' downgrades.

UBS Warburg cut profit estimates for PeopleSoft (PSFT: up $0.10 to $12.47, Research, Estimates), saying it believes the software maker will miss its target for the quarter due to a weak spending environment in its European market.

Separately, J.P. Morgan said it was still cautious on the market outlook, believing that equity valuations remain stretched. In a morning note, the brokerage house set a year-end 2003 target for the S&P 500 of 800 -- about 2 percent below current levels -- citing a weak earnings outlook. The firm also said a short-term relief rally was possible if the Iraqi situation is resolved.

European markets ended higher, while Asian-Pacific stocks finished mixed.

Treasury prices slumped, sending the 10-year note yield up to 3.72 percent from 3.59 percent late Monday. The dollar gained against the yen and the euro. Elsewhere, crude oil futures gained 38 cents to $30.83 a barrel in U.S. trading. Gold was lower.

Market breadth was positive. On the New York Stock Exchange, winners topped losers 2-to-1 as 1.6 billion shares traded. On the Nasdaq, advancers edged decliners as 1.7 billion shares changed hands.