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

The Institute for Supply Management said its measure of the service sector rose to 47.0 last month from 44.0 in May. That reading was above economists' median forecast for a rise to 46.0, but still below the dividing line between growth and contraction.

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.

Within the report, the business activity index jumped within a hair of expansion territory, to 49.8, from 42.4 in May.

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. And, the new orders component improved, Lantz said.

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.

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

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

Analysts are watching to see if the index can rise above 50 for several months for a trend to take hold.

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

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