Fresh dollar selling by exporters too aided the rupee rise while a firm dollar overseas capped the rupee rise.
FIIs had injected Rs 75.04 crore on Monday. The dollar index was up by 0.11 per cent ahead of data expected to show growth in the US economy, and the outcome of the Federal Reserve's two-day policy meeting which concludes later today.
At the Interbank Foreign Exchange (Forex) market, the domestic currency resumed lower at 60.21 a dollar from Monday's close of 60.13. It moved down further to a low of 60.24 on weak local stocks.
Later, the rupee rebounded in line with late recovery in equities to a high of 60.05 before settling at 60.06, showing a rise of seven paise or 0.12 per cent. This is its strongest level against the dollar since 59.93 on July 11.
The forex market was closed yesterday on account of "Ramzan Id".
The benchmark S&P BSE Sensex today broke its two-session losing string and rose by 96.19 points or 0.37 per cent.
Pramit Brahmbhatt, CEO, Veracity Group said: "Rupee continued to trade sideways and ended slightly better. The rupee is likely to trade range bound as investors are waiting for the RBI's credit policy scheduled on 5th August. The rise in local equities with the help of FIIs also helped rupee."
The trading range for the spot rupee is expected to be within 59.60 to 60.40, he added.
In the forward market premium closed weak on fresh receipts by exporters.
The benchmark six-month premium payable in December ended lower at 213.5-215 paise from Monday's close of 216.5-218.5 paise and far-forward contracts maturing in June, 2015 also declined to 464-466 paise from 469.5-471.5 paise.
The Reserve Bank of India fixed the reference rate for dollar at 60.1485 and for the euro at 80.6350.
The rupee also recovered smartly against the pound to 101.68 from 102.14 previously and also recouped to 58.75 per 100 Japanese yen from 59.06.
It, however, improved further against the euro at 80.49 from 80.79.