Initial reports suggested that the Spanish embassy was under attack, but Spain`s prime minister Mariano Rajoy denied this.
He later added that one Spanish police officer died in the attack.
The Taliban say their fighters detonated a car bomb in the Sherpur area and were currently inside a building there.
It is the latest in a series of audacious raids by Taliban fighters on high-profile targets in Afghanistan.
Casualties have been brought in to a nearby hospital, and eyewitnesses say a gun battle is still under way.
Eyewitnesses reported hearing a loud explosion followed by heavy gunfire on Friday evening.
Fresh gunfire and explosions were heard early on Saturday morning.
It follows a Taliban attack on Kandahar airport on Tuesday evening in which at least 50 people were killed.
Afghan security officials say that seven insurgents are involved in the attack. Both Afghan and Spanish security forces are reportedly at the scene.
"There has not been an attack, nor an attempt to carry one out on the Spanish embassy in Afghanistan" Mr Rajoy said.
"It was an attack on some guest houses that were very close to the embassy." he added.
Kabul police chief Abdul Rahman Rahimi told the BBC: " I can only confirm a suicide car bomb in the Sherpur area at this moment".
Freelance journalist Bilal Sarwary reported seeing two Spanish diplomats fleeing the compound shortly after the attack.
He saw one of them repeatedly bang their head on a vehicle in a show of grief.
Afghan police report that the militants had burned several armoured vehicles that they found inside the compound.
The initial explosion left two houses on fire, a police official told the Associated Press.
"It`s possible the attackers are hiding. We`ve blocked all the streets and are searching," he added.
Kabul attack: Taliban target embassy district
12 December 2015
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Taliban militants have attacked a foreign guesthouse in Kabul`s embassy district, causing several casualties.
