Washington said last week it was worried Russia was developing the system while saying it posed no immediate threat to people on Earth.
"We have always been categorically against putting nuclear weapons in space," Putin said in a meeting with Defence Minister Sergei Shoigu.
He called the accusations part of a "clamour being raised in the West."
Shoigu said Russia does "not have" the system Washington accused it of developing.
Putin said Russia has "many times suggested to strengthen join cooperation in the (space) sphere but for some reason in the West this topic has not come up again."
Russia's Ukraine offensive and huge Western sanctions hard hit Moscow's space sector and upended cooperation in space.
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