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.