Many financial markets were closed for the Good Friday Easter holiday.
Five banks agreed to pay EU fines of about $1.2 billion for colluding on forex trading strategies.
The rupee opened weak at 70.22 at the interbank forex market and then fell further to 70.32.
The fall reflects the IMF's condition for a "market-based exchange rate mechanism.
The yuan fell to its weakest level since December on Friday.
The rupee gained over 10 paise on Monday buoyed by RBI’s interest rate cut as well as lower oil price providing tailwinds.
This is the fifth successive session of gain for the domestic currency, during which it has climbed 62 paise.
Investors stayed away from risk-sensitive assets and bet on safe-haven dollar
The rupee firmed 6 paise at 63.85 against the dollar in opening trade today
The dollar gained 0.1 per cent versus the yen to 109.82.
This is the fourth successive session of gain for the domestic currency, during which it has climbed 49 paise.
The local currency on Thursday settled 11 paise at 71.45 against the US dollar.