The slowdown in factory output growth also led to the companies turning cautious on their hiring plans, HSBC said, while adding that RBI is likely to cut interest rate with inflation under control and growth losing steam.
The monthly HSBC India Purchasing Managers' Index (PMI) fell to 51.3 in June from 52.6 in May, largely because of the new orders rising at their slowest pace September.
"Following the pickup in growth rates for output and new orders seen in May, June PMI data pointed to a slowdown in India's economic upturn," said Pollyanna De Lima, Economist at research firm Markit, which compiles the data.
"New business expanded at a noticeably weaker pace, in part reflecting a loss of momentum in export business. Moreover, manufacturers remained in cautious spirits and employment numbers were unchanged once again," Lima added.
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On prices, it said the easing in inflation rates was a welcome move. Moreover, costs and charges both rose at rates that were historically muted.
In the June 2 policy review meet, RBI had cut repo by 0.25 per cent for the third time this year to spur investment and growth, but hinted that there may not be any more cuts in the near term.
RBI cut the repo rate (short-term lending rate) from 7.5 per cent to 7.25 in June, but left all other policy tools such as cash reserve ratio (CRR) and statutory liquidity ratio (SLR) unchanged at 4 per cent and 21.5 per cent, respectively.