In the offshore non-deliverable forwards, the one-month contract was at 61.56/66, while the three-month contract was at 62.16/26.
ICICI Venture denied the allegations, noting it had extended the lifespan of the Dynamic India Fund III by three years
The RBI's warnings signal its concern that unhedged firms could be a vulnerable link should global markets buckle.
A court ruled in favour of Vodafone on Friday in a long-running dispute with the Indian taxman, a boost for the British telecom group whose tax battles have been seen as emblematic of the troubles facing foreign investors in India.
The big test will come at the end of March when the fiscal year ends and banks tend to hold on to cash.
The tycoon had been allowed to use an office, phone, internet connection and three secretaries.
The rupee appreciated by three paise to close at one-week high of 60.81 against the US dollar in the previous session on sustained dollar selling by exporters and capital inflows.
Rajan also said the RBI had reduced the current account deficit "substantially".
India's macroeconomic indicators are improving and inflation has been coming down consistent with the central bank's forecast, but Asia's third-largest economy needs investment growth to pick up, he added.
Mallya, once known as the "King of Good Times" for his flamboyant lifestyle, has until Friday to appear before an IDBI committee to explain why he should not be declared a "wilful defaulter".
Roy and his associates were jailed in March after he failed to appear at a contempt hearing in the long-running dispute with the capital markets watchdog over the company's failure to repay billions of dollars to investors who were sold outlawed bonds.
The Reserve Bank of India (RBI) plans to impose stricter limits on how much a bank can lend to a single corporate group, a move aimed at curbing risk in the banking sector at a time when bad loans are on the rise.
The CBI has launched an initial probe over the loan against both companies, a spokeswoman for the agency said on Saturday.
Piramal, controlled by billionaire Ajay Piramal, and APG will invest in local infrastructure companies through rupee-denominated mezzanine instruments.
The rupee bounced back by 26 paise to end at 59.93 against the American currency on Friday as exporters and some banks sold dollars.
The rupee had revisited the near 2-month low of 60.55 per dollar earlier in the session.
The rupee had closed at 60.1550/1650 per dollar on Monday.
Increased selling of the dollar by banks and exporters amid sustained foreign capital inflows supported the rupee.
The bank adds it expects Modi to fight inflation through administrative measure
If completed, the move would create a 50-50 joint venture valuing Reliance Communications' cable assets at $1 billion.