As of 0511 GMT, the broader NSE index was up 0.37% at 10,781.75, while the benchmark BSE index was up 0.24% at 36,559.16. The indexes were lower by more than 0.80% in early trade on Friday.
Yes Bank Ltd was the top gainer on the NSE and BSE indexes, rising 6.7% after a series of sharp declines in recent sessions.
The NSE index was still on course to end nearly 3% lower for the week following three straight days in the red.
Other Asian markets also remained subdued, with uncertainty over how much further the U.S. Federal Reserve would cut rates added to caution caused by global growth fears.
MSCI's broadest index of Asia-Pacific shares outside Japan was higher by 0.08%.
A government official told Bloomberg News that India could announce a rollback of taxes for foreign portfolio investors (FPIs), BloombergQuint said in a tweet https://twitter.com/BloombergQuint/status/1164765591237873665.
A poorly received budget proposal on higher taxes for FPIs has contributed to a selloff in Indian markets, which has worsened amid an economic slowdown that has hit demand for everything from cars to underwear.
A series of meetings this month between Finance Minister Nirmala Sitharaman and FPIs, and between Sitharaman and Prime Minister Narendra Modi had raised hopes of stimulus measures.
But markets fell on Thursday after comments from India's chief economic advisor suggested that companies should not depend on the government for a stimulus and need to change their mindset.