He also said government forces suffered no casualties.
Special forces troops launched their ground operation on Friday after helicopter gunships opened fire on suspected anti-government forces, Kadyrov was quoted as saying by Interfax news agency.
It was not immediately possible to confirm the government's account of the attack.
Dmitry Medvedev, the Russian president, said on Thursday that instability in the North Caucasus region - which includes Chechnya, Dagestan and Ingushetia - was Russia's biggest domestic problem.
The patchwork of republics along Russia's southern flank has seen a wave of attacks in recent months that local leaders say are fuelled by a potent mixture of clan feuds, poverty, Islamism and heavy-handed tactics by law enforcement agencies.