Besides, future expectations for the business growth dipped to the lowest since February, raising concerns about sustainability of the economic upturn.
Experts also believe that rise in input costs may make it difficult for the Reserve Bank to lower the rates, given the central bank's priority to keep inflation in check.
The Nikkei Services Business Activity index, which maps the service sector activity, fell to 50.3 in June, from 51 in May. This marks the lowest level for the index in seven months and the second-lowest in a year.
"The Indian service sector saw a further cooling of growth momentum in June, the third in consecutive months, with a weaker rise in new business, leading to a softer expansion in activity," said Pollyanna De Lima, economist at Markit, which compiles the survey.
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In its last policy review meet in June, RBI Governor Raghuram Rajan kept interest rates intact, citing rising inflationary pressure, but hinted at a reduction later this year if good monsoon helps ease inflation.
The industry is still hopeful of further rate reduction from the apex bank to boost investment. The next policy review is scheduled for August 9, before which the PMI data for manufacturing and services for July would come out.
"Although manufacturing shifted to a higher gear in June, variables such as new orders, employment and production stayed below their respective long-run averages," Lima said.
On the jobs front, Indian service providers signalled a slight increase in staffing levels during June.
Moreover, future expectations came down to the lowest since February, highlighting concerns regarding the sustainability of the economic upturn, Lima added.
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.