WASHINGTON — The number of Americans applying for unemployment benefits fell 10,000 last week to a seasonally adjusted 340,000, a sign that employers are laying off very few workers.

The Labor Department said Thursday that the four-week average rose 8,000 to 356,250, the highest since April. The 16-day partial government shutdown and backlogs in California due to computer upgrades inflated the average.

Still, a government spokesman said those unusual factors did not affect last week’s first-time applications, which appeared to be free of distortions for the first time in two months.

Applications are a proxy for layoffs. They have fallen for three straight weeks and are just above the pre-recession levels reached in August.

Fewer applications are typically followed by more job gains. But hiring has slowed in recent months, rather than accelerated.

The economy added an average 143,000 jobs a month from July through September. That’s down from an average of 182,000 in April through June, and 207,000 during the first three months of the year.

Nearly 3.9 million people received unemployment benefits in the week ended Oct. 12, the latest data available.

That’s about 40,000 more than the previous week. But a year ago, more than 5 million people were receiving unemployment aid.

Hiring likely weakened even further in October because of the shutdown, which ended on Oct. 16. In addition to government contractors, other companies also likely cut jobs, such as restaurants and hotels located near national parks, which were closed. Some economists are forecasting that job gains in October could be 100,000 or less.

Payroll provider ADP said Wednesday that businesses added just 130,000 jobs in October. That’s down from ADP’s estimate of 145,000 private-sector jobs added in September.

The government will release its October employment report on Nov. 8. The report was delayed a week because of the shutdown.

The Federal Reserve said Wednesday that the economy is growing at a moderate pace but still needs its support.