MOSCOW (Reuters) - A recovery in business activity in Russia's services sector gathered momentum in June, the Markit purchasing managers index (PMI) showed on Tuesday.

The index's headline figure rose to 53.8 from 51.8 in May, moving further above the 50 mark that separates expansion from contraction.

The June reading was the second-highest for just over three years after a score of 54.2 in April.

Activity last month was supported by a continued rise in new business, although price pressures grew.

Tim Moore, senior economist at Markit, which compiles the survey, noted that caution about the business outlook was still holding back jobs growth.

The improvement in Russia's services PMI comes after a reading for the manufacturing sector also pointed to expansion in June.

The two surveys could revive hopes that Russia's economy is poised for recovery, following disappointing macroeconomic data in May.

The economy shrank 3.7 percent last year, hit by low oil prices and Western sanctions imposed because of the Ukraine conflict. Over the first five months of 2016 the economy contracted by 1.0 percent in year-on-year terms.

(Reporting by Alexander Winning; Editing by Hugh Lawson)