WASHINGTON » The number of Americans seeking unemployment aid plummeted last week to seasonally adjusted 339,000, the lowest level in more than four years. The sharp drop offered a hopeful sign that the job market could pick up.

The Labor Department said today that weekly applications fell by 30,000 to the fewest since February 2008. The four-week average, a less volatile measure, dropped by 11,500 to 364,000, a six-month low.

The positive figures follow a report last week that said the unemployment rate fell in September to 7.8 percent. It was the first time since January 2009 that the rate dropped below 8 percent.

A Labor Department spokesman cautioned that the weekly applications can be volatile, particularly at the start of a quarter. And the spokesman said one large state accounted for much of the decline. The spokesman did not name the state.

Unemployment benefit applications are a proxy for layoffs. When they consistently drop below 375,000, it suggests that hiring is strong enough to lower the unemployment rate.

Some economists said they want to see more data before suggesting the job market is turning around.

“Should this level hold for another week, it would flag a meaningful improvement in October” hiring, said Sal Guatieri, senior economist at BMO Capital Markets, in a note to clients.

Dan Greenhaus, chief market strategist at BTIG LLC, is also reserving judgment. “Are things that much better all of a sudden? Perhaps. We’re going to wait for some corroborating data.”

The total number of people receiving unemployment benefits also fell, the Labor Department said. A little more than 5 million Americans received benefits in the week ending Sept. 22, the latest data available. That’s down about 44,000 from the previous week.

Last week’s report noted that the unemployment rate declined to 7.8 percent in September from 8.1 percent in August because a government survey of households found that 873,000 more people had jobs. It was the biggest jump in nearly 10 years, although it was largely because of an increase in part-time employment.

Still, a separate survey of businesses showed that employers added only 114,000 jobs in September. That’s generally enough to keep pace with population growth but not enough to rapidly bring relief to more than 12 million who are unemployed.

Hiring over the summer was stronger than previously estimated. The economy gained an average of 146,000 jobs a month in the July-September quarter. That’s more than double the monthly pace in the April-June quarter.

Another report Wednesday suggested hiring will likely remain modest. Employers posted slightly fewer open jobs in August compared with July, the Labor Department said. It was the second straight monthly drop and the fewest openings since April.

A key problem is the economy is not growing fast enough to generate much hiring. Growth slowed to a tepid annual rate of 1.3 percent in the April-June quarter, down from 2 percent in the previous quarter. Most economists see growth staying at or below 2 percent in the second half of the year.