"Sulim died from his wounds in a Dubai hospital Monday," he said.
Yamadayev was shot by unknown assailants on Saturday.
The Russian consul general in Dubai has so far not confirmed if the victim is Yamadayev.
A RIA Novosti correspondent in the city of Gudermes has reported that Yamadayev's relatives in Gudermes are getting ready to pay their last respects.
Russia and the United Arab Emirates have yet to officially comment on the incident. The search for the attackers is ongoing.
Yamadayev was officially dismissed from his post as commander of the Defense Ministry's Vostok battalion last August over an alleged involvement in the 1998 abduction and murder of a Chechen businessman.
Yamadayev's brother Ruslan Yamadayev, a former member of the Russian parliament's lower house, was gunned down in central Moscow last September. He was a prominent opponent of Chechen President Ramzan Kadyrov, who has denied any involvement in the killing.
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Vladimir Putin Meets with Members of the Valdai International Discussion Club. Transcript of the Final Plenary Session
Vladimir Putin took part in the final plenary session of the Valdai International Discussion Club’s 11th meeting. The plenary session summed up the club’s work over the previous three days, which concentrated on analysing the factors eroding the current system of institutions and norms of international law.