Kumar congratulated Banerjee over telephone for Trinamool Congress' victory in the by-elections to one Lok Sabha and one Assembly seat, a statement from Kumar's office said.
Banerjee had recently called up Kumar over the Bihar crisis and assured to fight with him if BJP tried to impose President's rule in Bihar.
Kumar, who was locked in a fresh bout with rival BJP, had yesterday hailed the Shiv Sena for speaking the "truth" on BJP's role in Bihar's present political situation.
BSP supremo Mayawati had also called up Kumar on Sunday night and promised support against "BJP's gameplan to impose President's rule in the state."
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Congress, Samajwadi Party (SP), RJD and CPI have already supported Kumar in his fight to "foil BJP's gameplan" and to break the JD(U) by propping up Manjhi.
The Bihar crisis has also provided an opportunity for laying foundation for a broader anti-BJP platform.