On Sunday, Dubai police chief Lt. Gen. Dahi Khalfan Tamim accused Adam Delimkhanov, a Russian State Duma deputy since 2007, of involvement in the murder of Yamadayev. Delimkhanov served as Chechnya's deputy prime minister in 2006-2007.
"The Parliament of the Republic of Chechnya denounces as unacceptable such ungrounded accusations against a person known for his solid public position," the parliamentary statement said.
"[Adam] Delimkhanov together with federal political structures has devoted a great deal to the destruction of international terrorism and maintaining the territorial integrity of the Russian Federation and today represents the highest legislative branch of the country," the statement said.
The Chechen parliament said the Dubai police accusations were an "attempt to discredit...the entire state of the Russian Federation," adding that they were "trying to destabilize the political structure in Russia's south and the country as a whole."
Delimkhanov has called the accusations provocative and said he is willing to cooperate with the Dubai police in the murder investigation.
Tamim also said on Sunday that Dubai police had arrested two suspects in Yamadayev's murder, Mahdi Lournia from Iran and Makhsud-Jan, who is believed to be from Tajikistan. He added that several others would be put on Interpol's wanted list.
Yamadayev, 35, a Hero of Russia who commanded the elite Vostok battalion in Chechnya, was shot on March 28 by a lone gunman in the underground parking lot of the Dubai apartment building where he lived.
Yamadayev was officially dismissed as Vostok commander last August over alleged involvement in the 1998 abduction and murder of a Chechen businessman. The battalion, which answered directly to the federal Defense Ministry rather than Chechen authorities, has since been disbanded.
The killing of Yamadayev is the sixth in a series of killings of Chechens in the past year.
Sulim'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 either of the Yamadayev killings.