The benchmark S&P BSE Sensex trimmed its initial gains but was still higher by 74 points in late morning trade on Friday amid buying in healthcare, realty, metal and capital goods stocks.
Mild capital inflows from foreign funds also boosted the market to some extent.
Tata Power rose 1.33% ahead of its Q3 results on Friday.
The Sensex resumed higher at 20,441.04 points and hovered in a range of 20,450.51 and 20,363.62 before quoting at 20,384.42 points at 1030 hours.
It showed a gain of 73.68 points or 0.36% from its last close.
The NSE Nifty also moved up by 15.50 points, or 0.26%, to 6,051.80 at 1030 hours.
Besides Tata Power, the other gainers were Tata Steel (2.39%), Sun Pharma (2.24%), SSLT (2.10%), Dr Reddy's Lab (1.58%), Maruti (1.41%) and Axis Bank (1.08%).
Foreign Institutional Investors (FIIs) bought shares worth Rs 10.75 crore on Thursday, as per figures issued by stock exchanges.
Asian stocks rose in their early trade as US jobless claims fell and investors weighed company earnings.
Key benchmark indices in Indonesia, South Korea, Japan, Hong Kong, Singapore and Taiwan rose 0.53-1.81%.
After a rocky start to the week, US stocks roared back on Thursday, giving major stock indices their biggest gain of the year.
Meanwhile, the HSBC/Markit Services Purchasing Managers' Index (PMI) retreated to 50.7 in January, a low last seen in August 2011, though still above the 50-point level that demarcates growth and contraction.