Murthy, who founded India's second-largest IT services company Infosys, wanted a second term for Rajan for ensuring continuity in monetary policy and bettering growth rate.
"I would hope that the government would very respectfully request him to continue for one term or my preference would be two terms," he told ET Now.
Murthy joins the likes of CII President Naushad Forbes and Godrej Industries Chairman Adi Godrej in seeking a second term for Rajan, whose first three-year term comes to an end on September 4.
Rajan, who was appointed by the previous UPA government for a three-year term that began on September 4, 2013, has been under attack from some quarters in the BJP, including its Rajya Sabha MP Subramanian Swamy, for what they say his failure to lower interest rates and boost economic growth.
"I think the Governor has been doing a great job for the country and we would certainly see it as a very positive move if he were reappointed," Forbes had said.
Godrej had also said he is an admirer of Rajan and it will be a "good thing for India" if his tenure is extended.
"I think he has done a good job. He is very well respected across the world. He is a very capable person, very well respected person and I think if his term is extended, then it's a good thing for India," Godrej had said.
If denied an extension, he will be the first RBI Governor since 1992 not to have a five-year term.
His predecessors D Subbarao (2008-2013), Y V Reddy (2003-2008), Bimal Jalan (1997-2003) and C Rangarajan (1992-1997) had five-year terms.
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