Five police officers, one official from local emergency ministry and a civilian were killed, while the injured included both law enforcers and civilians, according to Kadyrov.
The first explosion occurred at 21:45 Moscow time (1745 GMT) when two police officers tried to detain a militant in the Chechen capital of Grozny.
Some 30 minutes later, the second blast followed as police and passersby gathered at the site.
Kadyrov told journalists on the night of August 30 that "the thugs have once again showed their true face" on a Muslim holiday Eid ul Fitr, "when people forgive each other and help the poor, orphans, and the sick."
A team of investigator has started probing into the explosion.
Violence is common in the North Caucasus republics of Chechnya, Dagestan and Ingushetia with militants frequently mounting attacks against police officers and authorities.
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