The blasts came a day after Interior Minister Nisar Ali Khan said a new security policy had been prepared for the safety of big cities and the army will also be part of patrols to check rebel attacks.
The first bomb exploded in the city's posh super market near a medical store, killing a security guard and wounding another, police said.
The bomb was hidden in a plastic bag and exploded when a security guard kicked it for checking, a police official said.
Shortly afterwards, the second explosion occurred in Karachi Company area of Islamabad.
The bomb was hidden in a vehicle parked outside another market. The explosion damaged the vehicle but no one was hurt.
Another police official said both were small bombs and 2-3 kg of explosives was used.
The third bomb hit a convoy of security forces in northwest Pakistan, killing six soldiers.
The improvised explosive devise (IED) was planted by militants in the troubled Mohmand tribal agency where security forces are battling Taliban militants.
Later, two security officials succumbed to their injuries in a military hospital in Peshawar, he said.
No one immediately claimed responsibility for the blasts, but authorities have blamed the Pakistani Taliban for similar attacks across the country.
The blasts came days after warplanes pounded militant hideouts in the North Waziristan tribal area bordering Afghanistan, killing at least 75.
The latest attacks were the first to strike the capital since an explosion tore through a bustling fruit and vegetable market in April, killing at least 23 people and injuring over 100.
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