A US think tank says a pro-war Russian figure has "openly criticized" President Vladimir Putin for withdrawing forces from the capital of the southern Ukrainian region of Kherson.

Russia's defense ministry on Friday announced completion of the retreat from Kherson city and other areas on the western bank of the Dnipro River.

The Institute for the Study of War says the pullout is "igniting an ideological fracture between pro-war figures" and Putin, "eroding confidence in Putin's commitment and ability to deliver his war promises."

The institute says pro-war ideologist Alexandr Dugin "openly criticized Putin ... for failing to uphold Russian ideology by surrendering Kherson City."

It adds that "Dugin said this Russian ideology defines Russia's responsibility to defend 'Russian cities' such as Kherson."

Kremlin spokesperson Dmitry Peskov stressed that the defense ministry decided on the move as part of the special military operation, and that inquiries should be made with the ministry.

Ukrainian President Volodymyr Zelenskyy said on Saturday that his troops had won back control of more than 60 settlements in the Kherson region.

Ukrainian troops are currently urging Russian soldiers who may still remain in Kherson city to surrender. Experts say some Russian soldiers may be blending in with Ukrainian civilians.