At the interbank forex market, the local unit opened at 73.80 against the US dollar, reflecting a rise of 5 paise over its last close. The local unit also touched a low of 73.86 in initial deals.
On Tuesday, the rupee had settled at 73.85 against the American currency.
The dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.09 per cent to 91.20.
Investors are focusing on the RBI Governor press conference. RBI has been in the process of assessing the exact impact of the COVID second wave, Kshitij Purohit, Lead International Products & Commodities at CapitalVia Global Research, said.
Governor Shaktikanta Das said RBI will continue to monitor situation from the resurgence of COVID-19 cases and will deploy all resources. ''We have to marshal our resources for fighting the virus with vigour,'' he said.
The Governor also announced Rs 50,000 crore priority lending by banks for hospitals and oxygen suppliers, among others by March 31, 2022.
A record 3,780 fresh COVID-19 fatalities were registered in a single day in India taking the death toll to 2,26,188, while 3,82,315 new coronavirus infections were recorded, according to the Union Health Ministry data updated on Wednesday.
Global oil benchmark Brent crude futures rose 0.71 per cent to USD 69.37 per barrel.
On the domestic equity market front, BSE Sensex was trading 169.95 points or 0.35 per cent higher at 48,423.46 while the broader NSE Nifty rose 52.10 points or 0.36 per cent to 14,548.60.
Foreign institutional investors were net sellers in the capital market on Tuesday as they sold shares worth Rs 1,772.37 crore, as per exchange data.