India's bond markets have rallied since last year on expectations the Reserve Bank of India will start cutting interest rates as early as February due to sharply easing inflation.
Dealers also expect RBI to try to prevent excessive strength in the rupee in a bid to help exporters remain competitive
The Reserve Bank of India sold dollars via state-owned banks around 62.3575 per dollar to contain the rupee's fall, traders said.
The central bank will come out with two measures on restructuring to tackle financial stress, Rajan said.
Large state-run entities and business houses will not be allowed to set up small finance banks, which will have to comply with statutory reserve requirements.
Indian companies are keenly waiting for reforms on rules related to land acquisition, labour, coal and power sector, and foreign direct investment in insurance sector.
The policymaker said the RBI had not reached the point where specific actions were under consideration.
In the offshore non-deliverable forwards, the one-month contract was at 62.26/36, while the three-month was at 62.83/93.
Consumer food price inflation, under a new series published by the government, eased to 5.59 per cent last month from 7.67 per cent in September.
The Reserve Bank of India (RBI) raised the minimum capital requirement for so-called shadow banks and tightened rules on deposits and bad loans to avoid any potential risk to the economy from these rapidly growing finance firms by regulating them like traditional banks.
Despite no change in interest rates, India's largest lender, State Bank of India, last week became among the latest to lower deposit rates, often a precursor to lower lending rates, something some banks have already done for certain consumer loans.
Foreign investors have bought around $2.4 billion in both debt and equity so far in October, pushing the total inflows to nearly $36 billion so far in the year.
The partially convertible rupee closed at 61.45/46 per dollar, weaker from Wednesday's 61.35/36.
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.
The RBI's warnings signal its concern that unhedged firms could be a vulnerable link should global markets buckle.
The big test will come at the end of March when the fiscal year ends and banks tend to hold on to cash.
Companies are legally allowed to invest in markets in India, but the practice has seldom stirred central bank concern until recently, when they have become much more active players.
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.