The bomber`s car struck Miryan police station on the outskirts of the town of Bannu and badly damaged a nearby mosque.
"We have received 18 dead bodies and 15 injured," said Mohammad Rahim, a doctor in Bannu`s main hospital.
District police chief Mohammad Iftikhar told AFP that most of those hurt were police officers and paramilitary personnel.
The attack was immediately claimed by Pakistani Taliban, who said it was to avenge US drone strikes in Pakistan`s tribal belt, which borders Afghanistan.
"We claim responsibility for this attack. We will continue such attacks unless the drone attacks are stopped," Taliban spokesman Azam Tariq, speaking from an undisclosed location, told AFP by telephone.
The bomb followed a missile strike by an unmanned aircraft on a militant compound in the North Waziristan region at dawn on Wednesday, which killed five militants, security officials said.
The United States does not officially confirm the controversial drone attacks, which take place with Islamabad`s tacit approval and which US officials say has severely weakened Al-Qaeda`s leadership.
In 2010 the campaign doubled missile attacks in the tribal area with around 100 drone strikes killing more than 650 people, according to an AFP tally.
The suicide attack came as US Vice President Joe Biden was visiting Pakistan and delivered a bold message of support for its key anti-terror ally, telling the country that America is "not the enemy of Islam".
Biden spoke following talks with President Asif Ali Zardari and Prime Minister Yousuf Raza Gilani that were expected to raise America`s wish to see Pakistan do more to eradicate Al-Qaeda and Taliban militants living on its remote border.
The United States wants Pakistan`s army to do more to combat extremists on its border, including by launching a ground offensive in the district of North Waziristan, where it says key Taliban leaders reside.
The army has stalled on a ground operation, saying its troops are overstretched. (*)
Editor: Kunto Wibisono
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