Sibal said other members of the panel, including lyricist Javed Akhtar, had written to him that they would like the actor to continue on the committee.
The minister said he told the actor that the none of the members has questioned his integrity and he should consider withdrawing his resignation.
Aamir resigned from the 10-member committee formed to look into the proposed amendments to the Copyright Act following the reported differences with Akhtar.
The actor said in his letter to Sibal that there was an attempt by certain people "to attack me in public by printing lies about me, thereby turning the attention away from a genuine debate about copyright issues".