"The recovery in the services sector gathered pace in January, with both business activity and new businesses accelerating," HSBC Chief Economist for India and Asean Leif Eskesen said in the report.

HSBC's business activity index climbed to 58 for January from 54.2 in December, it said.

"Growth in services along with manufacturing is rising sharply from the end-2011 lows. The upturn reflects an improvement in domestic demand as sentiment have recovered since the end-2011 when global wobbles and domestic policy paralysis held back demand," Eskesen said.

This is encouraging, as the bank had earlier this week reported that its manufacturing PMI reported a robust growth for the second consecutive month and moved up to an eight-month high of 57.5 in January from last month's 54.2.

The data came amid widespread concerns about sagging economic activity in the country, which is denting growth.

The survey of purchase executives from over 500 companies found a further increase in new orders in January due to a general improvement in demand and market conditions.

"Activity in the manufacturing sector rebounded again in January, led by higher demand from both domestic and foreign clients, suggesting some recovery in the sentiment in recent months," Eskesen had said.

On the back of the increase in both services and manufacturing activity, the HSBC India Composite Index moved up to 59.6 in January from 54.7 in December.

Work backlogs in the country's services companies reduced marginally in January and there was also a marginal increase in overall employment in the sector, it noted.

However, the bank notes that price pressure has not eased and said, "It is too early to cut policy rates."

"The RBI has already signalled a shift in its policy bias toward growth risks as demonstrated by the recent unexpected CRR cut," Eskesen said.

"However, underlying inflation pressures remain uncomfortably high... This limits the ability of the RBI to ease policies in the short-term and the RBI has also made policy rate cuts contingent on a sustained decline in inflation, fiscal consolidation and progress on key supply-side reforms," he said.

"We do not expect a policy rate cut until we enter into the April-June quarter," he added.

The bank expects growth to be constrained by the lagged effects of monetary tightening, administrative hurdles and weak global economic conditions.

It noted that key structural reform decisions will not be taken or announced with several state elections currently under way.