A weak dollar overseas also helped the rupee to land in positive terrain at the end while FII outflows of about R1,285 crore capped the rise, forex traders said.
At the Interbank Foreign Exchange (Forex) market, the domestic unit resumed better at 59.64 a dollar from overnight close of 59.68, also its all-time closing low.
The rupee moved in a range of 59.45 and 59.79 before settling the day at 59.66, showing a rise of two paise. Treasury managers said talks of RBI trying to defend the rupee whenever it approaches 60-levels helped the local currency. On Monday, it had fallen by 41 paise or 0.69%.
The dollar index was down by 0.15% against its major global rivals.
Bonds snap 3-day fall
Government bonds rose on Tuesday after three sessions of fall as buying emerged from domestic mutual funds following recent steep falls, though worries about continued foreign selling remain with the rupee still within sight of record lows.
The benchmark 10-year bond yield closed at 7.50 percent, 2 basis points (bps) below its Monday's close but up from the day's low of 7.46%.
The old 10-year paper, which is still among the most liquid papers, closed down 1 basis point at 7.68% after having dropped to as low as 7.63% earlier in the day.