"I invite human rights supporters from European structures and from Russia to come and look into any corner of the republic, to look into the presence of secret prisons, to study the condition of human rights," Ramzan Kadyrov said in a meeting with Chechen human rights activists.
Such an investigation could "close this question forever," Kadyrov said.
This week, the International Helsinki Federation human rights watchdog group urged European investigators probing allegations of secret CIA prisons in Europe to also look into the allegations against Chechnya.
Disappearances and allegations of torture and extrajudicial detention plague Chechnya as the republic's Kremlin-backed government tries to stifle a separatist insurgency that Russian forces have fought two wars against in the past 12 years.
Russian forces withdrew from Chechnya in 1996 after rebels fought them to a standstill in a 20-month war, but swept in again in September 1999. Large offensives are rare, but small clashes break out frequently and rebels target Russian forces with roadside bombs, booby-traps and hit-and-run shooting attacks.
Much of the republic is under firm Russian control, but its forces have been unable to wipe out rebels in Chechnya's southern mountains, where the rugged terrain gives cover to small guerrilla bands.
Kadyrov's father Akhmad, who was elected president in 2003, was assassinated in a bomb blast the following year. The younger Kadyrov since then has consistently risen in prominence, becoming prime minister this year.
Ramzan Kadyrov heads a security force that is widely alleged to kidnap and harass Chechens and that allegedly runs a clandestine prison in Tsenteroi, Kadyrov's home village.
The FSB of Russia has distributed the footage of video surveillance over suspects, who allegedly worked to orchestrate a military coup in Belarus and planned to assassinate its president, Alexander Lukashenko