The Nikkei Services Business Activity index, which maps the service sector activity, fell to 50.3 in June from 51 in May, one of the lowest readings in the current 12-month sequence of above-50 readings.
A reading above 50 represents expansion while one below means contraction.
"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," Pollyanna De Lima, economist at Markit, which compiles the survey, said.
The industry is still hopeful of further rate reduction from the apex bank to boost investment.
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Moreover, future expectations dipped to the lowest since February, highlighting concerns regarding the sustainability of the economic upturn, Lima added.
Meanwhile, the Nikkei India Composite PMI Output Index, which maps both manufacturing and services sectors, rose to 51.1 in June from 50.9 in May, but remained below its long-run average and pointed to a slight pace of expansion.
Lima further noted that "India remains a leading performer within emerging markets at a time when many of its peers are struggling."
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.