WASHINGTON (Reuters) - The number of Americans filing new claims for unemployment benefits rose last week, the Labor Department said on Thursday, but details of the report suggested the jobs market continued to grow at a moderate pace.

Initial claims for state unemployment benefits increased 4,000 to a seasonally adjusted 371,000, the Labor Department said. The prior week's figure was revised to show 5,000 fewer applications than previously reported.

Claims tend to be very volatile around this time of the year because of the holidays and seasonal layoffs, making it difficult to get a clear picture of the labor market's health.

While claims increased last week, there was nothing in the data to suggest a deterioration in labor market conditions.

The four-week moving average for new claims, a better measure of labor market trends, increased 6,750 to 365,750, still at a level consistent with steady job gains.

"Jobless claims data continue to suggest steady but modest U.S. employment gains," said Robert Kavcic, a senior economist at BMO Capital Markets in Toronto.

A Labor Department analyst said there was nothing unusual in state level data and that no states had been estimated. He noted, however, that jobless claims on an unadjusted basis tend to peak in the second week of January and the rise in the week ended January 5 was a build-up to that.

The labor market has been gradually improving, with job gains last year averaging 153,000 per month, little changed from 2011. That has not been enough to significantly cut the unemployment rate which ended the year at 7.8 percent.

The claims report showed the number of people still receiving benefits under regular state programs after an initial week of aid tumbled 127,000 to 3.11 million in the week ended December 29, the lowest level since July 2008.

Highlighting the typical volatility at the start of the year, the last time continued claims fell so much was in January 2011 and economists expect some correction in coming weeks.

The insured unemployment rate fell to 2.4 percent, its lowest since July 2008.

(Reporting by Lucia Mutikani; Editing by Andrea Ricci)