President Ramzan Kadyrov had earlier accused Sulim Yamadayev of involvement in a number of murders and kidnappings. Yamadayev was assassinated in Dubai on March 28.
"I have 70% proof that he was involved in the killing of my father, particularly as he tried twice to kill me, and wanted to poison a lake at my [Gudermes] residence on the day of my inauguration - I have witnesses," Kadyrov told reporters.
Ramzan's father, Akhmad Kadyrov, was killed in an explosion on May 9, 2004 in a stadium during a parade dedicated to the WWII victory. Fifteen other people died in the attack.
Yamadayev, 35, a Hero of Russia who commanded the elite Vostok battalion in Chechnya, was shot 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.