WASHINGTON — The number of people seeking unemployment benefits rose last week after three weeks of declines to a level consistent with modest gains in hiring.

But broader trend over the past month suggests job growth could pick up in the new year.

Weekly applications increased by 15,000 to a seasonally adjusted 381,000, the Labor Department said today.

Still, the four-week average, a less volatile measure, dropped for the fourth straight week to 375,000. That’s the lowest level since June 2008.

Applications generally must fall below 375,000 — consistently — to signal that hiring is strong enough to reduce the unemployment rate.

While layoffs have fallen sharply since the recession officially ended two and a half years ago, many companies have been slow to add jobs.

Still, hiring has improved in recent months. Employers have added an average of 143,000 net jobs a month from September through November. That’s almost double the average for the previous three months.

Next year should be even better. A survey of 36 economists by the Associated Press this month found that they expect the economy will generate an average of about 175,000 new jobs per month in 2012.

More small businesses plan to hire than at any time in three years, a trade group said earlier this month. And a separate private-sector survey found more companies are planning to add workers in the first quarter of next year than at any time since 2008.

In November, the unemployment rate fell to 8.6 percent from 9 percent. Still, about half that decline occurred because many of the unemployed gave up looking for work. When people stop looking for a job, they’re no longer counted as unemployed.

The pickup in hiring reflects some modest improvement in the economy. Growth will likely top 3 percent at an annual rate in the final three months of this year, economists expect. That would be better than the 1.8 percent growth in the July- September quarter.

Still, Europe is almost certain to fall into recession because of its financial troubles. And without more jobs and higher incomes, consumers may have to cut back on spending. Both could drag on growth next year.