NEW YORK — Stocks notched their first gain of the week Thursday after Spain announced severe budget cuts intended to convince the world that it can meet deficit-reduction targets.

It was the best day for the U.S. market since Sept. 13, when Federal Reserve Chairman Ben Bernanke announced further steps by the central bank to speed the economic recovery.

Stocks were also helped by speculation that the central bank of China will act soon to help the world’s No. 2 economy.

The Dow Jones industrial average climbed 72.46 points, or 0.5 percent, to close at 13,485.97. It was the Dow’s first gain in five trading sessions. The average was up as much as 109 points after the Spain announcement.

The Standard & Poor’s 500 index, after five days of declines, closed up 13.83 points, or just shy of 1 percent, at 1,447.15. The Nasdaq composite index rose 42.90 points to 3,136.60.

The Nasdaq and S&P were helped by a jump in Apple stock, reversing three days of declines. Apple gained $16.14, or 2.4 percent, to $681.32 despite an analyst’s report reducing estimates for shipments of iPhones later this year.

As fear grew that Spain will need an international bailout, the finance minister said a draft budget for 2013 cuts overall spending by (euro) 40 billion, or about $51 billion. He said cuts for ministries would average almost 9 percent.

The cuts are meant to show world investors and other countries that Spain can meet fiscal targets. The budget unveiling, shortly before noon EDT, lifted the U.S. stock market from what had been only modest gains.

“That’s the only major thing that’s happened,” said Dan Greenhaus, chief global strategist for the brokerage BTIG. “It’s an excuse to rally the stock market.”

Technology stocks and energy companies made the biggest gains. Utility stocks, which tend to do well when investors are fearful, were the only industry group in the S&P to fall.

The market gains started earlier, in Asia, helped by expectations that the People’s Bank of China will act soon. China’s biggest steelmaker said Thursday it has shut down a mill in Shanghai, a sign of weakening growth.

Stocks rose 0.5 percent in Japan and 1.1 percent in Hong Kong.

In the United States, investors grappled Thursday with mixed economic data:

— The economy grew at an annual rate of 1.3 percent from April through June, the government said, slower than the previous estimate of 1.7 percent and not nearly fast enough to reduce unemployment.

— Demand for long-lasting manufactured goods plunged in August by the most since January 2009. That was mostly because of a huge drop in commercial aircraft orders, which are volatile. Orders that reflect business investment rose solidly.

— The number of Americans seeking unemployment benefits fell 26,000 last week to 359,000, the lowest figure in nine weeks. A figure consistently below 375,000 is generally enough to lower the unemployment rate.

— The number of Americans who signed contracts to buy previously occupied homes fell in August from a two-year high in July. The National Association of Realtors’ sales index is still 10 percent higher than it was a year ago.

In Europe, stocks came back from one of their worst days in months. The benchmark stock index finished 0.7 percent higher in France and 0.2 percent higher in Germany and Britain.

Borrowing costs for financially troubled Spain and Italy also edged down, a positive sign.

In the U.S., demand for government bonds fell, generally an indication that investors are more willing to embrace risk. The yield on the 10-year note, which moves opposite the price, rose 0.03 percentage point to 1.65 percent.

The price of crude oil rose $1.87 per barrel to $91.85 as concerns mounted about a potential military confrontation over Iran’s nuclear program. Oil had dropped $9 a barrel in two weeks.

Israeli Prime Minister Benjamin Netanyahu warned at the United Nations that Iran will have enough enriched uranium to make a nuclear bomb by next summer and urged the world to draw a “red line” to stop it.

The dollar fell against the euro and pound but rose against the yen.

Among other U.S. companies making moves:

— Tempur-Pedic International, the mattress company, climbed $3.86, or 14.4 percent, to $30.64 after announcing it would buy a rival, Sealy, for about $229 million in cash.

— Discover Financial Services rose $2.69, or 7.3 percent, to $39.71. It reported a slight earnings decline in its latest quarter but beat Wall Street expectations. It also said credit card use increased and more customers paid off cards on time.

— GE hit a four-year high after the company told analysts it expects industrial revenue to rise about 10 percent this year. GE gained 63 cents, or 2.9 percent, to $22.73 in afternoon trading. They rose as high as $22.86.