Footage broadcast by Russian state television showed Putin kneeling at Karimov's flower-covered grave in the historic city of Samarkand after he made a detour to ex-Soviet Uzbekistan on his way home from the G20 summit in China.
Putin also held talks with Uzbek Prime Minister Shavkat Mirziyoyev, in a further sign that he is the frontrunner to replace Karimov, who was announced dead at 78 on Friday after a stroke with no clear successor.
But the Russian leader praised Karimov for maintaining "stability" and said Russia would "do everything to support the Uzbek people and the Uzbek leadership."
"You can count on us fully, as you can on your most faithful friends," Putin said, according to Interfax news agency.
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Mirziyoyev -- a Karimov loyalist known as a tough-guy enforcer -- told Putin that Uzbekistan's ties with Russia were "completely strategic" and that Tashkent would look to "continue to develop" them, Interfax said.
Footage also showed Putin greeting Karimov's black-clad widow Tatyana and younger daughter Lola inside a marble-lined hall before bowing his head in front of a large portrait of the deceased president.
Karimov was one of the Communist Party bosses who managed to cling to power after the collapse of the Soviet Union, crushing Islamist groups at home as he imposed his iron-fisted rule.
During his time at the helm, he kept the cotton-rich nation of 32 million balanced between Moscow and the West, at one stage hosting a US base for its operation in neighbouring Afghanistan.
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