Mann, who appeared before the Committee, expressed his readiness to give an unconditional apology if it felt he had made a mistake by recording a video of Parliament Complex and uploading it on Facebook.
But the panel expressed its displeasure over Mann's response, saying the AAP leader had mixed up his unconditional apology with references to Prime Minister Narendra Modi and the terror attack on the IAF base in Pathankot.
"This doublespeak is not acceptable to the Committee. He has been given 48 hours to present his case in writing. He has asked to appear before the Committee on Monday," a source told IANS.
Earlier, Mann, in a five-page letter to the Committee, said if the committee felt he had made a mistake, he was ready to tender unconditional apology.
But Mann insisted that Modi should also be summoned by the Committee as he had allowed Pakistan's intelligence agency ISI to visit the Pathankot airbase after the terror attack.
The nine-member panel is headed by BJP MP Kirit Somaiya.
The Committee is holding meeting daily as it has to submit its report by August 3 until when Mann has been told not to attend Parliament.
The Speaker said Mann's act of making a video had put the security of Parliament in peril.
The AAP maintains no security breach has taken place and that the Bharatiya Janata Party, the Congress and the Akalis had ganged up against the Lok Sabha member from Sangrur in Punjab.
On his part, Mann has maintained that he took a video of how members' questions for zero hour were subject to a lottery every day and that this was meant to educate his electorate.
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