The HSBC Purchasing Managers' Index for services business, based on a survey of about 400 private-sector companies, rose to 55.0 in August from 54.2 in July, marking nearly a year of uninterrupted monthly growth.
Services, including government services like railway transport, make up nearly 60 percent of India's economic output.
Stronger performance there could further dash already receding expectations for more interest rate cuts from the Reserve Bank of India, which is now widely expected to leave them on hold this month.
The new business sub-index rose to a six-month high of 55.9 in August after posting 55.7 in July while optimism for future business also bounced, registering its biggest monthly jump since April. Any number above 50 represents growth.
The Indian economy grew by 5.5 percent in the quarter to June on a year earlier, according to government data last week, slightly better than expected and above the previous quarter's nine-year low of 5.3 percent.
That suggested the worst of a growth slowdown that began in the quarter to June last year may be over.
But much depends on conditions overseas. The euro zone debt crisis, which appears to have driven it back into recession, along with weak growth in the United States, has dampened much of the export market for India.
Indian software firms, the face of the multi-billion dollar outsourcing industry, have suffered the most from wilting demand in Europe and the U.S. for new projects, leading to poor corporate results last year.
However, some firms are expecting some support to come from the many central banks around the world poised for more monetary easing.
Tata Consultancy Services, India's number one software exporter, announced in July that it expects this fiscal year to beat the industry export revenue growth forecast of 11-14 percent set by trade body NASSCOM.
In an indication of expectations for better times, Indian services companies added jobs at the fastest pace in over a year during August.
The survey also showed prices rose at a much slower pace in August. Input prices rose at their meekest pace since December 2009 while prices charged by firms increased at the slowest pace in over a year.
But persistent high inflation overall in India is not likely to ease any time soon, said Leif Eskesen, an economist at HSBC, citing wages in particular.
"With inflation risks still lingering, partly on the back of deficient monsoons, and policy inaction from Delhi persisting, the Reserve Bank of India has little room and appetite for rate cuts," Eskesen said in a statement.
India experienced inadequate rainfall this year in 13 regions, most of which are part of the country's agricultural belt, according to official data, suggesting food price inflation may accelerate.
A Reuters poll on Monday showed the RBI is expected to keep interest rates on hold when it meets later this month and economists only see a slight easing this calendar year. Policymakers appear concerned about inflation.
Inflation eased to 6.87 percent in August from 7.25 percent in July, but still remains well above the central bank's commonly perceived comfort zone of around five percent.
Growth in Indian manufacturing eased to a nine-month low in August as export orders fell for a second month, underscoring the risks to the wider economy from Europe's debt crisis, a sister survey showed on Monday.