Alkhanov said militants must be eliminated and that those who lay down their arms put on trial.
Alkhanov's election on 29 August came amid a devastating series of terrorist acts in Russia, beginning with the near-simultaneous downing of two passenger airplanes and ending with the hostage tragedy in Beslan, North Ossetia. More than 430 people were killed altogether.
Chechen militants claimed responsibility for all of the attacks. But Alkhanov told PACE that life is getting better in the republic: "Indeed, the situation in the Chechen Republic, the socio-political [situation], is complex. The criminal situation also is complicated. But, in general, both the socio-political and criminal situations in the Chechen Republic are under control and have firm, steady trends toward positive development."
Alkhanov also said the human-rights situation is also improving and that hostage takings have decreased this year.
Alkhanov's optimistic assessment contrasts sharply with PACE's own 36-page report, which describes the human-rights situation in the republic as catastrophic.
The Council of Europe, the 45-member pan-European rights watchdog, has repeatedly criticized rights abuses on both sides of the Chechen war, which has simmered since October 1999.
PACE has urged the Kremlin to stop widespread human-rights abuses, kidnappings, and torture in Chechnya. Rights groups say Russian troops and Chechnya's pro-Moscow authorities are responsible for many of the disappearances. PACE also condemned the hostage-taking in Beslan by Chechen militants and other such terrorist acts.
The Council of Europe's commissioner for human rights, Alvaro Gil-Robles, said today that kidnappings and murders must stop in the republic. He said federal authorities so far have failed to solve the problem of ending violence in the republic.
A rapporteur of the Committee on Migration, Refugees and Population, Tadeusz Iwinski, told the commission that the problem of refugees is one of the most urgent in the republic: "Over 350,000 persons have been forced to flee Chechnya since the beginning of the second war in 1999. Most of them have found refuge in neighboring Ingushetia, a considerably smaller number in Daghestan and other republics of the Russian Federation. Several thousands went to Central Asia, in eastern Kazakhstan, [and] to Western, as well as to Central Europe."
Iwinski said some refugees are returning home but that living conditions in the war-ravaged republic are dismal: "As for Chechnya itself, the living conditions of those who returned very often do not meet basic standards. Putting aside the security problem, the infrastructure, including access to health or education services, is inadequate."
On 6 October, Alkhanov said some 18,000 refugees have returned to their homes since April.
He said about 80 percent of Chechnya's industries and infrastructure have been destroyed by years of fighting in the republic, and that well over 50 percent of Chechnya's population is without permanent work.
(news agencies/RFE/RL's Russian Service)