The blasts in Jamrud area of Khyber tribal region, 30 km southwest of Peshawar, occurred when health workers were administering polio drops, said Jhangir Wazir, assistant political agent of the area.
Eleven paramilitary troops and a child were killed and 11 more were injured, sources said. The troops were guarding a convoy of vaccinators.
A vehicle carrying security personnel was destroyed while another was damaged in the attack.
The blasts were the latest attack on efforts to root out the crippling disease in Pakistan, which is one of only three countries where polio remains endemic.
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The fifth phase of an anti-polio drive began in Peshawar, the capital of Khyber-Pakhtunkhwa province, today amid tight security.
The administration imposed Section 144 CrPC and banned pillion riding on motorcycles to provide security for the campaign.
Nearly 4,500 security personnel have been deployed to provide security to vaccinators.
Dozens of health workers and security personnel have died in attacks on polio vaccination teams in the northwest and the port city of Karachi.