Besides, a higher opening in the equity market also supported the rupee, forex dealers said.
They, however, added that dollar's gains against other currencies overseas capped the local unit's gains.
Meanwhile, the BSE benchmark index Sensex rose by 51.16 points, or 0.27 per cent, to 18,875.07.
The rupee had edged up by 45 paise to close at an over five-month high of 52.40 against the dollar in the previous session on Monday on sustained capital inflows. The forex market remained closed yesterday on account 'Gandhi Jayanti'.