Asthana's promotion late last night was clouded by reports that a Central Vigilance Commission panel raised the issue of his alleged involvement in a corruption case.
"Please only ask questions related to it (matter on Jammu and Kashmir)," Singh said in response to a journalist's query on the officer's promotion.
He was addressing a press conference to announce a peace initiative on Kashmir.
Asthana, a 1984-batch IPS officer of Gujarat cadre, was working as additional director in the probe agency. He is the head of a Special Investigation Team (SIT) probing high- profile cases such as bank fraud case against Vijay Mallya and AgustaWestland VVIP chopper scam.
The Appointments Committee of the Cabinet (ACC), headed by Prime Minister Narendra Modi and having Rajnath Singh as its lone member, had approved Asthana's elevation.
In another tweet, Bhushan said, "Brazenness with which Modi govt violates law grows daily. ACC promotes offr as SPL Dir CBI in violation of SC orders (sic)."
"Amazing! Govt promotes Asthana as SPL Dir CBI, despite the CVC panel rejecting it because of lack of integrity! (sic)," he said in a separate tweet.
According to senior government officials, Asthana is tipped to be the next chief of the CBI.
The panel, which decides promotions and transfers of officers of the levels of Superintendent of Police and above in the CBI, has two vigilance commissioners Rajiv and T M Bhasin, home secretary Rajiv Gauba and Secretary of Department of Personnel and Training Ajay Mittal as its members.
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