The rupee was trading a tad weak at 64.12 on mild dollar demand from importers. However, dollar's weakness against other currencies overseas and a firm domestic equity market rendered restricted the rupee's losses.
The domestic unit opened strong by 5 paise at 64.05 at the Interbank Foreign Exchange market today. It hovered in a range of 64.14 and 64.05, before quoting at 64.12, down 2 paise at 4.35 pm local time.
Yesterday, the rupee had closed 4 paise at a near two-week high of 64.10 against the US currency.
The euro edged higher on Wednesday, recovering from the day's lows, though gains on strong private sector growth data from Germany remained muted as investors braced for speeches from European Central Bank President Mario Draghi this week.
The euro was trading 0.1 per cent higher at $1.1768 in early trade after weakening half a per cent against the dollar on Tuesday.
The dollar edged down against the yen on Wednesday after US President Donald Trump raised the spectre of a government shutdown to fulfil a campaign pledge, but overall moves among major currencies were limited ahead of this week's Jackson Hole global central bankers' conference.
The dollar index, which tracks the greenback against a basket of six major currencies, was flat on the day at 93.513 , after it gained 0.5 per cent in the previous session.
Meanwhile, the 30-share BSE index closed higher by 276.16 points or 0.88 per cent at 31,568.01.