At the interbank foreign exchange market, the rupee opened on a weak note at 70.96 and fell further to trade at 70.98.
A strengthening dollar against other overseas currencies also kept investors on the edge, forex dealers said.
However, strengthening of the greenback vis-a-vis other currencies overseas capped gains for the rupee, forex dealers said.
Easing crude oil prices propped up the local unit, though fresh capital outflows capped the gains, forex traders said.
Forex traders said rupee was trading in a narrow range as market participants remained cautious ahead of the Brexit summit.
Foreign fund inflows also supported the local currency, a forex trader said.
The rupee finally settled at 71.07, unchanged from its previous close.
Forex traders said most of the Asian currencies gained against the US dollar on China's offer to buy extra US goods.
Moreover, foreign fund outflows, heavy selling in domestic equities and rising crude oil prices also kept pressure on the Indian rupee.
Forex traders said, the rupee was trading higher as investors believe RBI will go for yet another rate cut to boost economic growth.