Three of the attackers blew themselves up, police said.
The same academy, the Manawan Police Academy, was attacked by a group of gunmen earlier this year, with 12 people dying in an eight-hour standoff.
Unconfirmed local television reports said that two people had been taken hostage.
"The enemy has started a guerrilla war"
Pakistan's interior minister
Another attack also took place on the Pakistani Elite Force Headquarters in Bedian, near Lahore, which assailants attempted to take over.
More than 20 gunmen stormed the building, with at least two policemen and five opposition fighters killed in the crossfire.
Police said hours after the attack that control have been regained in all three incidents.
Amjad Farooqi, of the Punjabi Taliban, claimed that the group was responsible for the three Lahore attacks.
Rehman Malik, Pakistan's interior minister, vowed not to let the attacks deter the government in its pursuit of Taliban and al-Qaeda fighters.
"The enemy has started a guerrilla war," Malik told a local television station.
Later in the day police reported a blast near a school in the northwestern city of Peshawar, in the busy Kohat road area, that injured five people.
Kohat suicide attack
On Thursday morning, a suicide bomber in a vehicle struck outside a police station in northwest Pakistan, killing at least eight people.
Civilians are believed to to have been killed in the blast on Thursday morning in Kohat near Peshawar, Habib Khan, a police official, said.
"It was a suicide attack," Dilawar Bangash, a district police chief, said.
"The bomber ploughed his car into the outer wall of the police station" he said, adding that the building was badly damaged.
In recent weeks, more than 100 people have been killed in suicide attacks, mostly claimed by the Taliban.
Imran Khan, Al Jazeera's correspondent in Islamabad, the capital, said that the style of attacks pointed to the work of the Taliban.
He also said of the FIA attack: "The real question is how were these people able to get into the building.
"This is an intelligence agency headquarters. It is a secure building that has been attacked before."
Imtiaz Gul, a political analyst in Islamabad, told Al Jazeera: "It seems that [opposition fighters] are taking advantage of the lack of leadership in Islamabad at the moment.
"The president [Asif Ali Zardari] and prime minister [Syed Yousaf Raza Gillani] do not seem to be in sync with the Pakistani military which looks embattled at the moment. And which is looking up to the political leadership to lead and consult them.
"Obviously these attacks are meant to prevent a ground offensive [by the army] in South Waziristan."
A suspected US drone attack also killed four people in North Waziristan, on the Afghan border on Thursday.
Two missiles struck a house 3km north of Miranshah, the principle town of the region, intelligence officials said.
At least three of the dead were Afghan Taliban members, the officials said.
"The owner of the house is a member of the Haqqani network," said one of the officials, referring to Jalaluddin Haqqani, a veteran Afghan commander.
The Haqqani network carries out attacks on foreign forces across the majority of eastern Afghanistan.
Alleged US drone attacks have increased since September 2008, as frustration has grown with Islamabad failing to eliminate Taliban hideouts on Pakistan's side of the border.
Hundreds of people have died, mostly opposition fighters, in the 42 drone attacks undertaken this year, including Baitullah Mehsud, a Pakistani Taliban leader.