A pair of near-simultaneous Taliban suicide bombings struck the Afghan capital on Wednesday, targeting a police station and offices of the country's intelligence agency and killing at least three people and injuring nearly 50, officials said.

In the police station attack, a suicide car bomber rammed his car into the gates of the station in western Kabul.

Najib Danish, deputy spokesman for the Interior Ministry, said the explosion was followed by a gun battle between police and an unknown number of attackers.

In the second attack, a bomber on foot detonated his explosives outside the offices of the intelligence service in eastern Kabul.

Ismail Kawasi, spokesman for the public health ministry said that at least three people were killed in both attacks. Mohammad Saber Nasim, head of a Kabul hospital, said nearly 50 wounded were brought to the hospital.

In a message to media, Taliban spokesman Zabihullah Mujahid claimed responsibility for both attacks.

It was not immediately clear how many gunmen were involved in the police station attack.

"We were in the dining room, eating lunch when a loud explosion happened. I couldn't see anything for a while," said Manizha, a policewoman who like many women in Afghanistan uses only one name.

She said she managed to escape from the compound as the gunbattle continued inside.

Thick black smoke rose above the police complex, and several rounds of small-arms fire and subsequent explosions were heard from inside the compound, according to Mohammad Naser, a shopkeeper who has a store nearby. Dozens of windows were shattered on surrounding houses and shops, he added.

The compound includes Kabul's so-called Sixth Police Station and is located next to the country's military school, which might have been the original target, along with cadets attending classes there.

Hours later, Sadiq Muradi of the Kabul police chief's office, said the gunbattle had ended and that security forces were carrying out a clean-up operation following the attack.

Danish, the ministry deputy spokesman, said that in the second attack, which took place in eastern Kabul when a suicide bomber on foot targeted the office of the national intelligence service, two people were wounded.

Afghan President Ashraf Ghani issued a statement condemning the attacks, saying that "terrorists and their alien masters once again tried to create an atmosphere of terror and fear in Kabul."

Ghani linked the attacks to the recent death of a senior Taliban commander, known as Mullah Salaam, in northeastern Kunduz province and claimed that insurgents are trying to attack urban centres to boost morale among their followers.

Meanwhile, the Taliban gained control Wednesday of local government headquarters in a district in northern Baghlan province, after almost three days of intense battles with Afghan security forces, according to local officials.

Abdul Satar Barez, the provincial governor, said he could not confirm that the whole district of Tala Wa Barfak has fallen to the Taliban but said a number of checkpoints have fallen to the insurgents amid clashes Wednesday.

A provincial security official said the security forces left their checkpoints and withdrew from the entire district, which is now in Taliban hands.

The official spoke on condition of anonymity because he was not authorised to talk to the media.

Mujahid, the Taliban spokesman, tweeted that their fighters have overrun the Tala Wa Barfak headquarters.