However, it was still well below the 54.3 it was at just before Prime Minister Narendra Modi's announcement on November 8 to ban high-value currency notes, which shocked the cash-reliant economy.
"Despite accelerating from April, rates of increase in both services activity and new work are much weaker than typical for India," said Pollyanna De Lima, an economist at IHS Markit.
A sister survey on Thursday showed factory activity growth cooled in May as new orders expanded at a more modest pace.
Taken together, they pushed the composite PMI, which includes both manufacturing and services, to 52.5 in May from 51.3, its highest in seven months.
Input prices rose for a ninth consecutive month but at a slower pace than in April. Companies were able to pass on only a small part of that to customers, pointed to continued pressure on profit margins.
Service providers were optimistic about growth in the year ahead, although the expectations index slipped to a three-month low.
"Business confidence fell as a reflection of firms' concerns regarding competitive pressures and lacklustre demand," Ms De Lima added.
India's economy grew 6.1 per cent from a year earlier in the January-March quarter, unexpectedly slumping to its lowest in more than two years and stripping the country of its status as the world's fastest growing major economy.
The Reserve Bank of India is not expected to make any changes to policy on Wednesday and to leave the repo rate at 6.25 per cent, despite inflation remaining below its medium-term target of 4 per cent, but will strike a less hawkish tone.
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