The currency is currently trading at 68.80 against the US Dollar.
Meanwhile, Government 10-year bond prices rallied as international crude oil prices declined after the US president Donald Trump threatened to place new tariffs on Chinese imports.
Further, India and the US need to "prioritise efforts" to manage current trade tensions and initiate cooperative projects in areas like intellectual property rights and digital trade, according to a report by a former trade official from the Trump administration.
The report, 'Trade at a Crossroads: A Vision for the US-India Trade Relationship', said it was clear that the first priorities for the future should be to manage current challenges and address those that were likely immediately ahead.
On a net basis, foreign institutional investors sold equities worth Rs444.99cr, while domestic institutional investors purchased shares to the tune of Rs637.71cr, provisional data available with stock exchanges showed Tuesday.
The local unit on Tuesday depreciated by 17 paise to close at 68.71/$ due to rising crude oil prices and foreign fund outflows.