The services sector data follows another monthly survey showing a similar trend in the manufacturing sector where output growth fell to five-month low in May.
The Nikkei/Markit Services Business Activity index, which maps the services sector activity, fell from 53.7 in April to 51.0 in May, pointing to a slight expansion in business activity which has been the weakest since last November.
A reading above 50 represents expansion, while one below this level means contraction.
"Latest PMI numbers raise doubts about the effectiveness of economic and monetary policies," Pollyanna De Lima, economist at Markit, which compiles the survey, said.
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Manufacturing production growth eased in May, which combined with the slowdown in services resulted in a weaker increase in private sector output, the survey said.
Lima further said that "ongoing weakness in manufacturing and services was evident in May, with output growth losing momentum for a second straight month. Overall expansion across the two sectors was the lowest since last November, as was the case for new orders".
"The gloomy growth picture will be a concern to policymakers and will raise the chances of further cuts in interest rates by the RBI," Lima said, adding "this would be supported by subdued inflationary pressures, with May data pointing to weaker increases in both costs and charges".
Earlier in April, the RBI cut its policy rate by 0.25 per cent to 6.5 per cent. While this was the first rate cut after a gap of six months, the RBI has lowered its rate by 1.5 per cent cumulatively since January 2015.
The PMI survey results show contrasting trends from what is being talked about the policymakers and several industry leaders, who are confident about an 8 per cent GDP growth in the current fiscal.
The official data released this week showed that the Indian economy grew at 7.9 per cent in the fourth quarter of 2015-16 taking the overall GDP growth to a five-year high of 7.6 per cent in the fiscal on the back of strong growth in manufacturing and services sectors.
"While monsoon, oil prices, and action of US Fed are imponderables for the RBI, the time is just right for another 25 basis points rate cut to give a fillip to India growth story that has started to gain momentum.
"Along with the rate cut, I also expect measures to make transmission of monetary actions more smooth and effective. We are already seeing signs of recovery in the housing industry and a rate cut at this juncture will surely give a boost to consumer confidence, encouraging them to invest in a home as loan rates soften," he added.