U.S. job growth increased only slightly last month and claims for jobless benefits rose last week, suggesting the labor market is slowing down, after strong growth early in the year.

In the week ending May 26, initial jobless claims rose by 10,000 to seasonally adjusted 383,000 from the previous week’s revised figure of 373,000, reported the Labor Department Thursday. It was the largest increase in claims since the first week of April.

The advance seasonally adjusted insured unemployment rate was 2.6 percent for the week ending May 19, unchanged from the prior week’s unrevised rate.

In a separate report, ADP employment in the private, service-providing sector increased 132,000 in May, after rising a revised 119,000 in April. Employment in the private, goods-producing sector increased 1,000 in May and manufacturing employment dropped 2,000 jobs, the second consecutive monthly decline.

The U.S. real gross domestic product (GDP) grew at an annual rate of 1.9 percent in the first quarter of 2012, according to today’s second estimate. This follows a growth rate of 3.0 percent in the fourth quarter of 2011.