The Congress, on the other hand, said that if the TMC so decides, it can go ahead and fight alone.
"It has been proved by the results of these elections that the Trinamool Congress has enough strength to rule Bengal alone", the party's all-India general secretary Mukul Roy told a press conference after results were out for the six civic bodies in the state.
"It has been established that in Bengal that Trinamool can fight and win elections alone. We fought against CPI(M), Congress, BJP and the Maoists", Roy, also the Railway Minister, said.
"The results have shown that not only CPI(M), but there are some other parties which are going to be insignificant in Bengal politics", Roy said.
"The results of the civic polls have proved that the people are with Trinamool Congress and again they have shown confidence in the leadership of Mamata Banerjee", he claimed.
Reacting to Roy's statement, state Congress president Pradip Bhattacharya said, "If they (TMC) have decided to fight alone, let them fight alone. God bless them. We have not said we will fight alone".
He said that if that situation indeed appeared, the Congress would also fight the election.
Congress MP Adhir Chowdhury said that its convincing victory at Cooper's camp proved that Congress could also fight alone.
Though allies in the central and state governments, Trinamool Congress and Congress contested the civic elections separately.
On Congress retaining the Cooper's Camp civic body in Nadia district, Roy said it was a "stray happening" and is "not significant".