Raghuram Rajan, whose current three-year tenure ends on September 4, has already said no to a second term.
Swamy had also claimed that Rajan was "mentally not fully Indian" and alleged that he has "wilfully" wrecked the economy
The RBI targets inflation at 6 percent by January 2016 and 4 percent for 2017/18.
Raghuram Rajan's three-year term is the shortest of any G20 country and the recent governors have been given second terms as much as seven months in advance.
Making light of his critics, he also said there are people who send him 'anonymous thank you notes' even when he on a plane.
Rajan was speaking at a news conference.
Reiterating his earlier stance, BJP's Rajya Sabha member Subramanian Swamy has written a letter to Prime Minister Narendra Modi, asking him to sack RBI Governor Raghuram Rajan.
Rajan, the academic-turned-central banker who is credited with predicting the global financial crisis, said that voicing of views will have positive effects.
Reserve Bank Governor Shaktikanta Das on Tuesday said the fiscal-monetary coordination was at its best during the last six years even as he thanked Prime Minister Narendra Modi for giving the opportunity to head the monetary authority of the country. Das, in a series of posts on X, on his last day of his six-year term as RBI Governor, also thanked the Finance Minister, various stakeholders and his colleagues at the central bank.
Rajan's comment comes against the backdrop of certain BJP leaders questioning his policies to deal with the current economic woes.
RBI Governor cautioned against more volatility.
The RBI Governor also reiterated his reservation against repeated loan waivers by various state governments, saying the move distorts credit pricing, thereby also disrupting the credit market.
Business houses expect rate cut in next RBI policy.
All eyes are on new Reserve Bank Governor Raghuram Rajan who will come out with his maiden monetary policy review on Friday amid conflicting demands for rate cut and an urgent need to contain inflation which soared to 6-month high of 6.1 per cent in August.
'Rajan brought in a healthy air of competition in the banking sector.'
Prime Minister Narendra Modi defended Mr Rajan, but it would be debated why he took so long to dub criticisms like those against the RBI governor as improper.
Reserve Bank Governor Raghuram Rajan on Friday said banking sector will see major changes in the coming years.
As the global economy sways into uncertain territories and domestic prices almost certain to rise, Raghuram Rajan's ideas would have come in handy.
Former Prime Minister Manmohan Singh's 1991 budget unshackled India's economy, significantly enhancing the economic prospects for hundreds of millions of Indians, first deputy managing director of the International Monetary Fund (IMF) Gita Gopinath said on Friday.
RBI Governor Raghuram Rajan's decision to not seek a second term is a "personal one" which everybody should respect, Chanda Kochhar MD & CEO, ICICI Bank said.
A panel headed by Reserve Bank of India deputy governor Urjit Patel recommended in January moving to an inflation target.
Rajan said the relationship between the RBI and the government has been strong.
Rajan, a professor at the University of Chicago, said if the money raised by the government was not spent, it could result in inflationary pressures, pushing up real interest rates. The problem could get aggravated if foreign capital flows rose, said Rajan, who was in Mumbai to deliver a lecture.
Analysts say the RBI could resume tightening monetary policy by early next year should inflation remain high, even as the economy is growing below the decade low of 5 percent posted in the fiscal year ending in March.
Seeking to guard investor returns from excessive exchange rate movements, RBI Governor Raghuram Rajan on Thursday said a move towards an inflation target of 4 per cent will help contain the currency market volatility.
The mid-year analysis lowered the growth projection for the current financial year to 5.7-5.9 per cent from 7.6 per cent estimated earlier.
Former RBI governor Raghuram Rajan has asked why SEBI has not yet got to the bottom of ownership of the four Mauritius-based funds who are said to have parked 90 per cent of their $6.9 billion in Adani group stocks, saying does the market regulator need help of investigating agencies for this? The funds -- Elara India Opportunities Fund, Cresta Fund, Albula Investment Fund and APMS Investment Fund -- have been under cloud for last couple of years after allegations that they may be shell companies. They came into focus once again in January when a US short seller alleged that Adani Group used offshore shell companies to inflate stock price.
Raghuram Rajan said on Friday it is not clear India needs a so-called "bad bank.
The comments assume importance as the traditional position of the central bank has been not to set a forex reserves target.
'There has been an enormous amount of attention paid to issues like capital account convertibility, bank privatisation and bank priority sector norms. There are many other areas where reforms are less controversial, but perhaps as important,' the report of the high-level Committee on Financial Sector Reforms headed by Raghuram Rajan, a professor at Graduate School of Business, University of Chicago, said.
Former RBI Governor Subbarao blamed Chidambaram for undermining the autonomy of RBI and putting pressure on him to cut interest rates.
Rajan encouraged the Indian-American business community to get involved in the 'nitty gritty of the implementation process,' saying such involvement was not difficult especially since the Indian government has the political will to reform.
Rajan posed the question while speaking at the annual leadership conference in Mumbai National Association of Software and Services Companies.
Rajan said an interest rate cut won't by itself lead to higher economic growth
A high import of the metal is putting pressure on current account deficit.
The core inflation is down and there is a need to push growth.
'There are lots of low hanging fruits and often no real impediment to plucking them.'
The Reserve Bank of India Governor Raghuram Rajan said bringing down inflation would help stabilise the rupee.
RBI governor highlights the role of fate in his career at a meeting of the IIM-A alumni.
The rupee has gained 1.89 percent against the dollar in the month to date and 2.93 percent in the past six months.