The head of police of the Leninsky district and his driver were taken to the hospital in serious condition after a bomb in a street drain went off as their car drove past, the agency said, quoting Chechnya's interior ministry.
The blast injured around a dozen people, including two Russian soldiers in an armored personnel carrier, and left a huge crater in the road near the interior ministry building.
A Reuter correspondent at the scene said hats belonging to the soldiers lay on the ground near the damaged military vehicle and passenger car. The area was cordoned off by police.
It was the latest in a series of bomb attacks in the Chechen capital which began with a blast in September aimed at President Boris Yeltsin's representative in Chechnya, Oleg Lobov.
Lobov escaped injury but the following month Moscow's military commander in the region, General Anatoly Romanov, was badly injured in another explosion. He is still in a coma.
Moscow blamed separatist leader Dzhokhar Dudayev's rebels for the bombs. They have denied responsibility.
In a separate incident, Russia's military command in Chechnya said Friday a Finnish aid worker representing the International Organization for Migration had been killed.
The man, named as Matti Aho, was killed on Thursday in the town of Shali, about 25 kilometers southeast of Grozny, Tass quoted the armed forces' press center as saying.
The Finnish embassy in Moscow said Aho was in his 30s and had been working in Chechnya as a humanitarian aid supervisor since October. It had no further details of his death.
The International Organization for Migration is a Geneva-based organization which works alongside the United Nations to help displaced people.
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