The attack in a prosperous business and residential area of the capital took place just hours after a Taliban suicide attack near the Defence Ministry killed at least 24 people, including a number of senior security officials.
Fraidoon Obaidi, chief of the Kabul police Criminal Investigation Department, said one of the two gunmen who had entered an office of Care International in Kabul had been killed but another was holding out.
"We have rescued several families from the area," he said.
The attacks highlighted the precarious security climate in the capital just a month before a conference in Brussels where international donors are expected to pledge continued financial support to Afghanistan.
After several hours of quiet overnight, sporadic gunfire and explosions could be heard as day broke. Security officials evacuated terrified civilians from their offices and homes near the explosion site.
An Interior Ministry official said initial reports indicated one person had been killed and six wounded in the attack, with 31 people rescued from the area.
Kabul traffic was blocked in several parts of the city and schools in the area were closed.
On Monday, 24 people were killed and 91 wounded when twin blasts in quick succession tore through an afternoon crowd in a bustling area of the city close to the Defence Ministry.
"When the first explosion happened people crowded to the site and then the second blast occurred, which was really powerful and killed lots of people," said Samiullah Safi, who witnessed the attack.
An army general and two senior police commanders were among the dead, a Defence Ministry official said. Another official said the deputy head of President Ashraf Ghani's personal protection force had also been killed.
The double bombing came less than two weeks after gunmen attacked the American University in Kabul, killing 13 people.
It was the deadliest attack in Kabul since at least 80 people were killed by a suicide bomber who targeted a demonstration on July 23. That assault was claimed by Islamic State.
The Taliban's ability to conduct coordinated high profile attacks in Kabul has piled pressure on the Western-backed government, which has struggled to reassure a war-weary population that it can guarantee security.
Afghanistan's foreign partners, concerned about the ability of the security forces to withstand Taliban violence, are expected to pledge support over coming years at the Brussels conference, three months after NATO members reaffirmed their commitment at a meeting in Warsaw.
Outside Kabul, the insurgents have stepped up their military campaign, threatening Lashkar Gah, capital of the strategic southern province of Helmand, as well as Kunduz, the northern city they briefly took last year.
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