Forex traders said the 21-day lockdown imposed by Prime Minister Narendra Modi showed that the government is willing to take hard steps to fight the Covid-19 pandemic.
At the interbank foreign exchange the rupee opened at 75.90, then gained further ground and touched a high of 75.81 against the US dollar, registering a rise of 13 paise over its previous close.
On Tuesday, rupee had gained 26 paise to settled at 75.94 (provisional) against the US dollar after Finance Minister Nirmala Sitharaman said the government is working on an economic package to deal with the coronavirus crisis.
Forex market was closed on Wednesday on account of Gudi Padwa.
The assurance of domestic stimulus by the government boosted investor sentiment. However, there are concerns over the impact of coronavirus outbreak on the domestic as well as global economy.
The number of deaths around the world linked to the new coronavirus has crossed over 21,000. In India, more than 600 coronavirus cases have been reported so far.
Meanwhile, domestic bourses opened on a positive note on Thursday with benchmark indices Sensex trading 561.80 points higher at 29,097.58 and Nifty up by 516.80 points at 8,317.85.
Foreign institutional investors (FIIs) remained net sellers in the capital market, as they sold equity shares worth Rs 1,893.36 crore on Wednesday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, fell 0.51 per cent to USD 27.25 per barrel.
Meanwhile, the dollar index, which gauges the greenback's strength against the basket of six currencies was trading 0.30 per cent lower at 100.75.
The 10-year government bond yield was at 6.31 per cent in morning trade.