Pranab, who is also the chief of the Congress in the state, accepted the failure of his party in the elections held to 81 municipal bodies, including the Kolkata Municipal Corporation (KMC), ahead of next year's crucial assembly polls.
"I would like to congratulate Mamata Banerjee for her excellent performance," Mukherjee said, accepting that the Congress has done "badly" in the elections.
"I accept the verdict of the people," Mukherjee said.
The Trinamool Congress won the KMC elections with a huge margin. The initial results of other municipal corporations across the state also indicate a victory for the party.
The elections were held a year after the Lok Sabha polls that saw the Trinamool Congress-Congress combine along with the Socialist Unity Centre of India decimate the ruling Left Front.
But the political equations have substantially changed this time around. The Trinamool Congress and the Congress failed to clinch a seat-sharing deal.