Rebel groups have given a boycott call of Independence Day celebrations in the state, as they had done in earlier years.
The bomb, an improvised explosive device (IED), exploded around 6.20 pm in front of the City Convention Centre, close to Singh's official residence and the state police headquarters, officials said.
The rebels planted the IED under the footpath in front of the convention centre and possibly used a remote control device to explode it, sources said.
Today's explosion followed a grenade blast in front of Singh's residence on August 10 for which the People's Revolutionary Party of Kangleipak-Progressive (PREPAK-P) had claimed responsibility.
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It was not immediately known how the insurgents infiltrated into the high-security area and planted the bomb.
Insurgents have been boycotting Independence and Republic Day celebrations for more than three decades.
The sources said police would investigate to find out if there was any lacunae in the deployment of the forces as there has been 24-hour patrolling in the capital complex.