In his condolence message, Kumar described Castro as a "revolutionary leader" and a "successful administrator".
The JD(U) president said he had a chance to meet Castro during a World Youth festival in Hawana in 1978.
Former Union minister Natwar Singh said the Cuban leader stood by India through thick and thin.
"I had the privilege of meeting him 6-7 times both in Havana and Delhi...He was a very good friend for India. He stood by us through thick and thin," he said.
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Leader of Opposition in Andhra Assembly Y S Jaganmohan Reddy said Castro kept the Communist flag flying for decades.
"He showed the world how a small country could live on its own terms without bowing to external pressures," Jagan said in a statement.
AP Congress president N Raghuveera Reddy and vice-president S Sailajanath also mourned Castro's demise.
Castro, who led a rebel army to improbable victory in Cuba, embraced Soviet-style communism and defied the power of 10 US presidents during his half century rule, died Friday night at age 90.
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