However, firming oil prices capped the gains, traders said.
A weak trend at the domestic equity markets and global trade tensions kept sentiment subdued, traders said.
Strengthening crude oil prices and a stronger greenback in global markets, however, kept the rupee rise in check.
Foreign institutional investors pulled out Rs 401.99 crore on Monday, hitting the rupee sentiment.
Domestic bourses was trading in the negative territory on Friday with benchmark indices Sensex trading 362.28 points lower.
The rupee opened weak at 68.55 at interbank forex market and then fell further to 68.70, down 20 paise over its last close.
At the interbank foreign exchange, rupee opened stronger at 68.83 and went on to touch the day's high of 68.79.
At the Interbank Foreign Exchange, the rupee opened at 69.02 then fell to 69.05 against the US dollar.
Silver ready prices declined by Rs 260 to Rs 38,570 per kg, while weekly-based delivery reduced by Rs 295 to Rs 37,157 per kg.
On a weekly basis, the Indian Rupee has gained 55 paise.