Washington ? American manufacturers saw demand for their products rise modestly in May, raising hope that this battered sector of the economy may be emerging from a rough patch.

New orders placed with U.S. factories rolled in at a total value of $320.6 billion in May, representing a 0.4 percent increase from April’s level, the Commerce Department reported Wednesday.

The increase comes after orders fell by a sharp 3 percent in April from March, the steepest decline since November 2001.

“There is a glimmer of hope that manufacturing is beginning a return to a growth track after a disastrous, war-influenced April time-out,” said Ken Mayland, president of ClearView Economics.

On Wall Street, stocks were lifted by the report. The Dow Jones industrial average soared 101.89 points to close at 9,142.84.

May’s performance turned out to be stronger than the flat forecast economists had been making.

Even so, while happy with the improvement in factory orders in May, Mayland and other economists said there was still reason for caution.

“These figures, however, paint a picture of a skeptical factory sector,” Mayland added. “Nobody is sticking his neck out to take any chances on a recovery.”

Manufacturing has been hard hit by the uneven economic recovery. Faced with sluggish demand at home and abroad as well as competition from a flood of imports, manufacturers have throttled back production and cut jobs.

Businesses — wanting profits to improve — have been reluctant to crank up capital spending and to go on a hiring spree, two crucial ingredients to a sustained turnaround for the national economy.

Against that backdrop, the Federal Reserve last week decided to cut a key interest rate by one-quarter percentage point to 1 percent, the lowest level seen in 45 years. Its hope is that lower borrowing costs might rev up business investment and consumer spending and give a boost to economic growth.

In Wednesday’s report, the 0.4 percent increase in factory orders was helped out by stronger demand for nondurable goods, a category that includes apparel, food and plastic products.

In that broad category, orders placed to factories rose by 1.2 percent in May, a turnaround from April’s 3.7 percent decline.

Also helping out was an 0.8 percent increase in May for new orders for furniture and related products, following a 3 percent advance in April. Demand for these goods partly stems from brisk home sales, a bright spot for the economy. When people move into a new or previously owned home, they often need some new furnishings, analysts said.

However, orders for household appliances, computers and cars all posted declines in May.

Excluding orders for transportation equipment, including automobiles, which tend to swing widely from month to month, orders placed to factories rose by 0.8 percent in May, compared with a 2.7 percent drop in April.

The factory orders news comes one day after a report showed that manufacturing activity was sluggish in June.

The Institute for Supply Management’s manufacturing index rose to 49.8 last month, up from 49.4 in May. A reading below 50 means manufacturing activity is slowing; above 50 indicates the industry is growing.

Although June’s performance was weaker than expected, some economists said that the fact that the index went up rather than down offered some hope that the battered manufacturing sector may be stabilizing.

“The data of late on manufacturing show me that while we are firming up a bit — we are really not going anywhere,” said Clifford Waldman, economist at Manufacturers Alliance/MAPI, a research group. “The good news is that there’s some stability in the picture, but the bad news is that I don’t see anything beyond a weak manufacturing recovery in the next couple of quarters.”