Activity in India's service sector expanded at the fastest pace in a year last month, driven by rising foreign orders, but businesses were a little less optimistic about the future, a survey showed on Tuesday.

The HSBC Markit services Purchasing Managers' Index, which gauges business activity from a survey of over 400 companies ranging from banks to hospitals, jumped to 57.5 in January from 55.6.

The services PMI has held above 50, the level that divides growth and contraction, for over a year, even though India appears set to finish the 2012/13 fiscal year with its slowest economic growth rate in a decade.

Services make up over 60 percent of Asia's third-largest economy. Some of India's top services exports are software, back-office support and banking services.

"Service sector activity continued to pick up pace led by a faster inflow of new business," said Leif Eskesen, HSBC's chief economist for India and Southeast Asia, in a release.

The new business sub-index jumped to 58.3, the highest since August 2011, prompting firms to step up the pace of hiring, although not at a very strong rate.

Although companies were optimistic about the future, the business expectations index fell slightly from December.

The survey also showed input and output prices rising at a similar pace to the prior month, though much weaker than a year ago.

Wholesale price inflation eased to a three-year low of 7.18 percent in December, giving the Reserve Bank of India room to cut its key lending rate by 25 basis points to 7.75 percent last week.

"Inflation readings held broadly steady, with fuel, raw material and labour cost pressures still simmering. These numbers underscore the need for the RBI to approach policy easing with caution," said HSBC's Eskesen.

The RBI is expected to cut the repo rate by another 75 basis points to 7 percent by September.

Manufacturing activity grew in January at its slowest pace in three months, a similar survey showed last week.