In active trade at the Interbank Foreign Exchange market in Mumbai on Tuesday morning, the rupee opened distinctly firm at 44.15/18 per dollar and firm up further to 44.07/09 in late morning deals, steeply higher from Monday's close of 44.25/27 per dollar.
Recovering a major part of last week decline, the rupee on Tuesday rose by 18 paise due to sustained heavy FII inflows and trade remittances.
Relatively cool global oil prices hovering around $41.33 a barrel also helped market sentiment, a dealer said.
Foreign funds have pumped in $7.76 billion into the Indian share market so far in the current calendar year. Forex reserves were at record $130.72 billion as on December3.
"The rupee will strengthen further on the back of rising FII inflows and may revisit the $44 again," another dealer said.
The rupee spurted by a massive 50 paise on Monday buoyed by robust weekend dollar supplies from FII and trade inflows.
Turning to cross currency trades, the euro was quoted at Rs 58.67/69, pound sterling at Rs 84.81/83 and the Japanese yen (100) at Rs 42.06/08.