The HSBC Services Purchasing Managers' Index (PMI) , compiled by Markit, rose to 48.3 in January from 46.7 in December.
While the reading is the highest in seven months, it has been stuck below the 50 mark that separates growth from contraction for just as long.
In contrast to the services PMI, a sister survey on Monday showed Indian factories had a good start to 2014 with activity growing at its quickest pace in nearly a year.
"Service sector activity remains weak and broad based ... Meanwhile inflation pressures firmed, with input prices rising at a faster pace," said Leif Eskesen, chief economist for India at survey sponsor HSBC.
Input prices rose at their quickest pace in three months and firms again passed some of those rising costs on to customers, albeit at a slightly slower rate than in December. The input prices subindex leapt to 54.7 from 52.8.
This adds to India's existing worries including a slowdown in economic growth, fragile global demand for the country's goods and services, and more recently, a selloff in emerging markets as the U.S. Federal Reserve tapers its stimulus.
Late last month, the RBI surprised markets by raising the repo rate to 8 percent to battle inflation and said it was better prepared to deal with any risks to the economy from the selloff.
India's consumer price inflation eased to a three-month low in December and the RBI said at its January meeting it was unlikely to hike rates again if retail inflation eased as expected.
Still, HSBC's Eskesen expects the RBI to maintain a hawkish stance.
"Despite the weak growth backdrop, the RBI has to stick to its hawkish bias to get inflation under control and through this eventually pave the way for a recovery in economic activity," he said.