Telecom, financials and capital goods counters saw some action.
Participants are tracking the appointment of new US Federal Reserve chief and Republicans' unveiling of massive tax cuts.
The 30-share Sensex resumed higher, but moved between 33,692.58 and 33,531.94 before trading at 33,627.10 at 1311 hours, up 53.88 points, or 0.16 per cent.
The broader NSE Nifty rose 20.40 points to 10,444.20, up 0.20 per cent.
Major gainers were Axis Bank, Cipla and ONGC, with gains of up to 1.88 per cent.
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Foreign portfolio investors (FPIs) bought shares worth a net Rs 1,032.88 crore yesterday, as per provisional data released by the stock exchanges. Domestic institutional investors (DIIs) sold shares worth a net Rs 456.51 crore.
In the US, the Dow Jones Industrial Average closed at a record yesterday, but the other main benchmarks were muted as investors sifted through tax reforms details.