The fighting erupted shortly after a suicide bomber rammed a vehicle into a police station in another part of the valley, killing eight policemen.
"The entire building was demolished after the explosion ... people are searching for bodies inside the rubble," Kamal Hyder, Al Jazeera's Islamabad correspondent, said.
The attack on the police station took place in the town of Chaharbagh, Mohib Ullahn, a police official, said.
Muslim Khan, a Taliban spokesman, immediately claimed responsibility and vowed more attacks if the government did not halt army operations in the area, which used to be a popular tourist destination.
Bridges destroyed
Another attack, less than an hour later, in the in the town of Barikot killed two people and injured three.
In the attack, a remote controlled bomb exploded at an abandoned police station, killing an eight-year old girl and a man and injuring four others, a police officer said.
"Four bridges [in the Swat Valley region] have also been blown up - this would be an attempt by the so-called Taliban to try and disrupt military movement but this is also causing difficulties to the local population and most of the policemen killed today were also locals, " Hyder said.
As a result "this is giving rise to speculation among security analysts, that the so-called Taliban are not from the area and that is why they are killing indiscriminately," he said.
Pakistan's military says it has killed up to 16 armed men in the country's northwest, including a would-be suicide bomber.
A military statement said the fighting broke out on Friday when security forces stopped a vehicle at a checkpoint near the town of Hangu in the North West Frontier Province.
One person who got out of the vehicle and moved towards the checkpoint was shot by troops, the statement said, subsequently detonating explosives he was carrying.
"In the ensuing gunbattle, 15 militants were killed and one was arrested alive," AFP news agency quoted Sher Bahadur, a local police officer, as saying.
Major-General Athar Abbas, Pakistan's chief military spokesman, confirmed the incident but did not provide further details.
Fighters also fired rockets overnight at a police station in Bada Bahr, near the northwestern city of Peshawar, killing one policeman and wounding two others, police said.
Bajaur crackdown
In the adjoining region of Bajaur, one of Pakistan's semi-autonomous tribal zones, military helicopters on Friday killed another five armed men, officials said.
A military offensive in Bajaur in the past two weeks has left more than 500 people dead, most of them suspected Taliban fighters, officials say.
Three men were killed when military aircraft destroyed their vehicles as they were driving outside Bajaur's main town of Khar, an unnamed security official told the AFP news agency.
Two more men died when helicopters targeted a compound in Salarzai village, the official said.
On Thursday, a double suicide bombing killed 64 people at a major arms factory in the town of Wah, about 30km from Islamabad, the capital.
A spokesman for Tehreek-e-Taliban Pakistan, the umbrella group for the country's pro-Taliban movement, said that attack was a response to military operations in Swat and Bajaur.
Police said a young man, suspected to be a would-be suicide bomber, was caught trying to flee the scene of Thursday's blasts.
Mohammed Saeed, a local police official, said that police had recovered an explosives-packed jacket that the suspect was believed to have left in a mosque's toilet close to the factory.
"The army and police arrested a suspected bomber not far away from scene of the attack," Saeed said. "They also recovered a suicide jacket from a nearby mosque and seized explosives."