54 against the dollar on Monday on growing demand for dollars among oil importers, while the greenback was also boosted by upbeat US jobs data.
The partially convertible rupee hit its previous low of 57.32 against the dollar on June 28 last year.
On Monday it fell to a new record low before trading up slightly at 57.49 later in the morning.
The fall is the latest blow to the damaged growth story of India, Asia's third-largest economy, which has been beset by sharply slower growth, worsening public finances and political turmoil.
The rupee depreciated seven percent against the dollar in May, similar to other Asian currencies.
"The dollar strengthening is hurting the rupee," said Naveen Mathur, commodities and currencies associate director with Angel Broking, who said the Indian currency unit showed "continuous weakness".
With the US economy improving, there is growing debate that the US Federal Reserve could "reverse" its monetary stimulus programme sooner than expected.
Analysts fear that the slide for the rupee is unlikely to slow down.
Abhishek Goenka, chief executive of consultancy firm India Forex Advisors, exp