Taliban fighters have a significant presence in the area, the officials said.
"The armed militants attacked the post killing all [four] policemen inside," Adialat Khan, a local government official, told the AFP news agency.
He said the post, set up to conduct security checks on the main road heading into Khar, was destroyed.
Official confirmation
Other security officials confirmed the incident, which came after another government official said fighters abducted a policeman in Mamoun, 15km northeast of Khar.
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Pakistani security forces launched a huge operation against fighters in Bajaur last August.
In February, they claimed the area had been cleared after months of fierce fighting, but unrest has persisted.
The attack in Bajur shows the difficulties Pakistan is facing as it battles al-Qaeda and the Taliban who have long enjoyed a safe haven in the area.
The US and Pakistan's other Western allies are pushing Islamabad to undertake sustained action against the Taliban blamed for attacks that are destabilising the country as well as neighbouring Afghanistan.
'Fighters killed'
In the tribal district of Orakzai, south of Pakistan's main northwestern city of Peshawar, more than 10 fighters were killed in air raids late on Thursday, military and government officials said.
"Militant compounds and hideouts were targeted in the attacks. More than 10 militants were killed in the bombing," a military official told the AFP.
It was the second bout of Pakistani air raids in Orakzai following the deaths of at least 26 security personnel in a helicopter crash in the area.
The Taliban claimed responsbility, saying it shot down the MI-17 to avenge an offensive in South Waziristan, the heartland of Baitullah Mehsud, Pakistan's Taliban warlord.
But the military blamed the July 3 incident on a technical fault.