Rights groups, like the independent Russian organization Memorial, claim Kadyrov's special police force is behind many of the kidnappings and violent acts that continue to terrorize the republic's civilians.
The Russian Interior Ministry says that some 600 people were kidnapped in Chechnya last year, although Memorial and others estimate the number is much higher.
Aleksei Malashenko, a political analyst at the Moscow Carnegie Center, said Kadyrov's all-Chechen force is a well-armed group, composed of many former rebels, with considerable fighting experience. Modest estimates put the size of the force at some 4,000 fighters, answerable directly to Kadyrov and his son, Ramzan.
Malashenko said the Kremlin has sought to have Kadyrov's force placed under its control, but such a move has proven complicated while fighting is still raging in Chechnya.
One thing is certain, according to Malashenko -- Kadyrov's police inspire even more fear in the republic than Russian forces do.
"It is completely true that they are feared more than Russian special forces, because the police have a very different agenda," Malashenko said. "To begin with, the force consists of people who are personally loyal to Kadyrov and fulfill his specific orders. That is very clear. Secondly, these are people who [are former rebels, who] after several different amnesties, came down from the mountains and who are now being given an opportunity to settle scores with those who were fighting against them back then."
Malashenko said Kadyrov's police take advantage of their unofficial status to settle various tribal and family disputes, often on Kadyrov's behalf. In this way, the analyst said, the force essentially functions as a private presidential army.
Kadyrov's son Ramzan is particularly feared within the organization, and is believed to have ordered numerous kidnappings and torture, in addition to operating a private prison.
Still, according to Aleksei Makarkin, an analyst at the Moscow-based Center of Political Technologies, the situation is better for many civilians than the mop-up operations conducted by Russian troops in the past.
Because Kadyrov's police forces are acquainted with the local population, they are better able to discriminate between regular civilians and resistance fighters. Their methods may be vicious, Makarkin said, but any other option would be worse. "Was there an alternative? Is there an alternative? The alternative in this case has helped to stop massive, targeted mopping-up operations," Makarkin said.
Observers say Kadyrov's force is so strong it might eventually threaten the Kremlin's vision of a compliant Chechen leader. They say Kadyrov might eventually break ties with Moscow, much as Dzhokhar Dudaev -- the first separatist Chechen president -- did in the 1990s.
Makarenko, however, said that for now, the true ruler of Chechnya remains the Russian Army. Without the presence of Russian troops, he said, the entire power system in the republic would collapse.
"This entire system completely depends on Russia for its material support, military support," he said. "Let's not forget that even putting aside all those factors, Russian regular forces are based there."
As the struggle for power continues, and amid Kadyrov's pledges of security, the fighting continues unabated in Chechnya. Rebel attacks yesterday left a reported seven Russian soldiers dead, and wounded 14 more.