The U.S. service sector was still shrinking last month but at a slowing pace, with activity at the highest since September 2008, when Lehman Brothers' collapse exacerbated the global financial crisis, a report showed on Monday.

At the same time, a separate measure of job growth fell slightly in June from May's level.

The Institute for Supply Management said its measure of the service sector rose to 47.0 last month from 44.0 in May. The reading was above economists' median forecast for a rise to 46.0, but it was still not indicative of a definite turnaround.

It's a good number, not quite showing expansion yet, but rising closer to that 50-level that divides contraction from expansion, said Gary Thayer, senior economist with Wells Fargo Advisors in St. Louis.

The services sector represents about 80 percent of U.S. economic activity, including businesses such as banks, airlines, hotels and restaurants.

Both manufacturing and service sector reports show signs that the 18-month-old U.S. recession, the most protracted in decades, may soon end.

The ISM service sector report's business activity index jumped within a hair of expansion territory, to 49.8, from 42.4 in May.

The new orders index rose to 48.6 in June from 44.4 in May. Prices paid rose to 53.7 in June from 46.9, driven partly by a rise in oil prices, said Anthony Nieves, chair of the ISM non-manufacturing business survey committee.

Analysts are watching to see if the index can climb above 50 for several months to confirm a new trend is taking hold.

I don't want to get too excited until I see what the next couple of months brings, ISM's Nieves said.

Much depends on the labor market. Though the job market is usually a lagging indicator that recovers after recessions end, some analysts worry that the weakest labor market in a quarter century may curb economic growth or even catapult the economy back into recession.

U.S. stocks initially pared losses after the ISM data, while government bond prices dipped. The dollar trimmed losses against the yen.

The ISM report showed jobs in the services sector contracted, but at a slower pace, with the employment index rising to 43.4 in June from 39.0 in May.

The details were pretty solid, with the employment number improving, said Carl Lantz, U.S. interest rate strategist with Credit Suisse in New York. The non-manufacturing ISM tends to track payrolls pretty well, which suggests that perhaps July won't be as bad as June on that front, Lantz said.

The widely watched government non-farm payrolls report released on Thursday showed that U.S. employers cut 467,000 jobs in June, far more than the expected 363,000.

On Monday, a research group said the U.S. job market weakened in June after rebounding in May for the first time in 21 months.

The Conference Board, a private research organization, said its Employment Trends Index slipped to 88.4 from a downwardly revised 89.1 in May. It was originally reported at 89.9.

Compared with the beginning of the year, the decline in the Employment Trends Index has significantly moderated, said Gad Levanon, senior economist at the Conference Board. We therefore expect job growth to resume around the end of the year.

However, he added, over the last month, leading indicators of employment were mostly disappointing, suggesting the Employment Trends Index is still seeking a bottom.

(Additional reporting by Camille Drummond, Ellen Freilich and Burton Frierson; Editing by Dan Grebler)