The Prime Minister said that all pertinent records and documents available with the government have already been placed with the JPC.
"I have received your letter of 1 April, 2013 regarding the Joint Parliamentary Committee looking into the 2G matter," Singh said in his letter to Sinha.
"You are aware that all pertinent records and documents available with the Government have already been placed at the disposal of the JPC. I have said from the beginning that neither the Government nor I have anything to hide in this matter," the PM said.
"The decision as to what evidence should be sought and which individuals should be asked to appear before the JPC is a matter that needs to be decided internally by the JPC and its Chairman," he said.
Sinha on Monday wrote to Singh and asked him to appear before the JPC looking into the 2G scam.
In his letter, Sinha, a member of the JPC, said any hesitation on the PM's part to appear before the panel will prove that he has "something to hide".
Sinha said that when Parliament's Public Accounts Committee (PAC) was examining the Comptroller and Auditor General (CAG) report on the 2G scam, the Prime Minister had publicly offered to appear before it to enable the committee to reach the "right conclusions".
"You have not made a similar offer to the JPC despite the fact that many members of the JPC have publicly demanded that you appear before the JPC," Sinha said in his letter to PM Singh.
The opposition leader claimed that in his statements to the JPC, former telecom minister and key accused A Raja has levelled "serious allegations" against the Prime Minister and Union Finance Minister P Chidambaram.
"I think it is in your own personal interest to appear before the JPC and clear your name. You may also suggest the Finance Minister to make a similar offer," Sinha wrote.
Sinha also asked the Prime Minister to request JPC Chairman PC Chacko to call Raja as a witness before the committee, after hitting out at the Congress leader for not doing so himself, earlier in the day.
The BJP on Tuesday said Singh should depose before the JPC looking into the 2G scam.
"PM must depose before JPC on 2G Scam," BJP Spokesperson Nirmala Sitaraman said while addressing a press conference here.
"Yashwant Sinha, who is also a member of the JPC, has very aptly said that the Prime Minister should appear before the JPC," she said.
In perhaps the biggest scam in Independent India, allegedly masterminded by Raja, telecoms spectrum was given away at throwaway prices in 2008 causing a potential revenue loss of up to Rs 1.76 lakh crore.
Raja, who had languished in New Delhi's Tihar jail for 15 months in connection to the scam, was released on bail last year. He was arrested in 2011.
A landmark judgement by the Supreme Court last year had quashed 122 licenses issued under the sale.