Forex traders said trading in emerging market currencies were subdued tracking cautious opening in domestic equities.
At the interbank foreign exchange, the rupee opened at 71.97 and declined to 72 against the US dollar.
The rupee had closed at 71.84 against the US dollar on Monday.
Traders awaited fresh cues on the potential US-China trade deal.
Meanwhile, Brent crude futures – the global benchmark for crude oil – fell 0.24 per cent to $62.29 per barrel.