The Central Bureau of Investigation moved the petition Monday when Jagan was presented before the court and his judicial custody was extended till June 25.
The agency said in its petition that it needed to do the test on the accused to take the investigation forward. It complained that Jagan gave evasive replies and unless narco test was done, he ws not likely to answer all the queries.
Jagan's counsel opposed the CBI petition and argued that it may be treated as contempt of court in view of the Supreme Court guidelines on narco test.
He said the CBI deliberately moved the petition to pressurize Jagan as its similar petition for narco test on Vijay Sai Reddy was already dismissed.
The judge asked Jagan's counsel to file a counter to the CBI petition and adjourned the hearing to June 14.
In February, the special court had refused to grant permission for narco test on Jagan's aide Vijay Sai Reddy, who is number two accused in the case.
The court had ruled that as per the guidelines of the Supreme Court the test can't be conducted without the consent of the accused.
The CBI, which questioned Jagan three days before his arrest May 27 and for another seven days after he was sent to judicial custody, found him a hard nut to crack.
While seeking two-day custody last week, the agency had told the high court that Jagan gave irrelevant answers to its questions during five-day custody earlier.
The investigating agency had questioned him with regard to the investments made into his firms by the companies, which benefited from the then government of his father Y.S. Rajasekhara Reddy.
He was also grilled about the investments flowed into his business through hawala.