Before the meeting, Hungarian Prime Minister Viktor Orbán had appealed for the release of prisoners of war who hold citizenship in both Hungary and Ukraine.
Putin claimed upon their release that the two prisoners had been forced to fight for Ukraine.
In the conversation with Orbán - who is under pressure from opposition leader Péter Magyar ahead of the parliamentary elections on April 12 - Putin is said to have thanked Hungary for the country's "principled" policy on Ukraine.
Hungary is blocking a recent multi-billion-euro loan from the EU to Ukraine, as well as the latest sanctions package against Russia.
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