Survivors pray over the bodies of the dead
The first exploded under a bus carrying pro-Moscow police while the second ripped into a police vehicle rushing to the scene in the centre of the capital, Grozny.
It appeared the explosions were deliberately timed to coincide with Mr Putin's mid-term state-of-the-nation address, which they preceded by two hours.
Addressing both houses of the Russian parliament, Mr Putin said that the time had come to focus on reconstruction of the shattered republic's infrastructure and judicial system.
Government criticised
He also accused his government of a lack of ambition, saying that it needed to aim for higher economic growth, and called for the country's "cumbersome, inflexible and ineffective state apparatus" to be overhauled.
Thursday's blasts in Grozny - just 200 metres from the Interior Ministry headquarters - come after six Russian soldiers were killed on Wednesday by two separate mine blasts south of the capital.
According to one report as many as 21 people died.
Russian troops responded by blocking all main routes out of the city, in an attempt to trap the killers.
Thousands of Russian soldiers remain in the republic, two years and six months after they poured over the border to restore Moscow's control.
But Russian soldiers and representatives of the pro-Moscow Chechen authorities continue to die on an almost daily basis.
"Only a year ago we were counting how many people we were up against, how many bandits and terrorists there were - 2,000 or three, five or 10. Now we're not bothered how many there are. What we need to know is where they are," Mr Putin said in his address on Thursday.
"The main task at the current stage is to restore Russia's political and legal space in Chechnya, to create effective legal institutions and law-enforcement structures of Chechnya's own."
Poverty
At the same time he acknowledged that "bandits" were continuing to disturb the lives of civilians.
Despite criticising the Russian Government for lack of ambition, Mr Putin acknowledged that life for many Russians was improving.
Unemployment was down by 700,000 he said, incomes had risen by nearly 6%, and people were beginning to believe they had a future.
But, he added, 40 million Russians were still living in poverty.
Estimates suggest Russian economic growth slowed to 5% in 2001, after hitting a record 9% in 2000.
Kremlin adviser Andrei Illarionov has suggested a growth target of 8%, but Russia's Economic Development and Trade Minister, German Gref, has argued that aiming for rapid growth could destabilise the country.