Forex traders said rupee along with most Asian currencies strengthened following dovish comments from New York Fed officials.
Traders said foreign fund outflows and cautious opening in domestic equities weighed on the local unit.
Forex traders said cautious trading in the domestic equity markets also weighed on the local unit.
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.