The incidents happened in the southern province of Helmand on Friday night and followed a spate of violence in the troubled south, police officials in the province said on Saturday.
They said five insurgents died in one of the attacks.
Seven police officers were killed in Hazar Joft district after dozens of insurgents raided and burned the district and police headquarters, and the other two died in a raid in Baghran district, they added.
Six police officers were wounded in the Hazar Joft attacks, district police chief Haji Bahadur said.
"Apart from our casualties, five Taliban were killed,too, in the fighting," Bahadur said.
But a Taliban spokesman, Qari Mohammad Yousuf, said Taliban fighters killed 10 police officers and only one insurgent had died.
Helmand was a key Taliban bastion until US-led forces overthrew their government in 2001.
The attacks followed a flare-up of violence in the past week in which Afghan and US military officials said at least two dozen Taliban fighters were killed in adjacent Kandahar and Uruzgan provinces.
At least 10 soldiers from the US-led foreign force battling the insurgents were wounded in clashes.
There are about 30,000 US and
Nato soldiers in Afghanistan
About 20,000 mostly US troops are hunting the Taliban and their allies, including Osama bin Laden and his al-Qaida fighters.
Friday's violence came a day after Nato, which leads a separate peacekeeping mission in Afghanistan, approved rules for an expanded force next year, which Washington hopes will allow a cut in US troop levels in the country.
Nato wants to boost its 9000-strong International Security Assistance Force to about 15,000 from early next year. It will spread its bases in the north and west, and the capital, Kabul, to the more volatile south.
Nearly 60 US soldiers have been killed in Taliban-linked violence this year, mostly in the south and east, the bloodiest period for US forces since the Taliban's ouster.