The benchmark BSE Sensex closed 32.46 points higher at 10,162.16 on the Bombay Stock Exchange on Thursday due to buying by funds and retail investors.
It had touched 10,326.05 points earlier in the day.
Similarly, the National Stock Exchange index Nifty closed up by 16.80 points at 2997.90, after touching a high of 3049.25.
Earlier, tracking global trend, the index was up by over 164 points in early trade.
The Sensex, which had closed nearly 21 points lower in volatile trade on Wednesday, was up 164.70 points at 10,294.40 in first five minutes of trading.
Similarly, the Nifty index on the wide-based National Stock Exchange gained 50.25 points at 3031.35.
All the 30-index related stocks were in the green with sizable gains.
Infosys Technologies was up by Rs 47.25 at Rs 3020, Reliance Industries by Rs 20.20 at Rs 1021, Larsen and Toubro by Rs 50.50 at Rs 2120 and ONGC by Rs 30.80 at Rs 1064.