"I appeal to him to kindly withdraw his resignation," Advani said in a statement.
Hegde had alleged that there was rampant corruption in the southern state, including in the government, which was making it difficult for him to function and submitted his resignation.
"I have known Justice Santosh Hegde for a long time. He is an eminent jurist for whom all of us have great respect. As Lokayukta of Karnataka, he has certain concerns, I am sure the state government of Karnataka will address them earnestly," Advani said.
There were requests from several quarters, including from Karnataka Chief Minister B S Yeddyurappa and Union Home Minister P Chidambaram, to Hegde asking him to take back his resignation.