The car bomb blast shook Shash Darak, a heavily fortified area adjacent to the Green Zone and home to several important complexes including the National Directorate of Security, the Afghan intelligence service.
Apparent surveillance footage of the attack, which occurred at about 10:10 am (0540 GMT), showed a grey minivan explode just after it had cut in front of a line of white SUVs waiting to make a right turn onto a street.
One nearby pedestrian can be seen turning and trying to run away as the minivan crashed through a barrier just before the blast.
Resolute Support, the US-led NATO mission in Afghanistan, said a Romanian and an American service member had been killed in the explosion.
The American death brings to at least 16 the number of US military killed in action in Afghanistan this year, just as Washington is seeking a way out of its longest war.
According to interior ministry spokesman Nasrat Rahimi, at least 10 people were killed and 42 more wounded.
On Twitter, Taliban spokesman Zabihullah Mujahid claimed responsibility for the attack, saying a "martyrdom seeker" -- or suicide bomber -- had triggered the car bomb and that "foreign invaders" were killed.
Massoud Zazai, who owns a photo studio across the street from the blast site, said he was in his shop when the explosion happened.
"I fell off my chair and it got dark inside the shop because of smoke and dust," Zazai told AFP.
"I went out to the scene moments after the attack. The side of the road was littered with debris and bodies."
Through the smoke, Zazai said he could hear injured people crying and calling for their mothers and brothers.
"It was horrifying," he said.
The attack was close to where an Islamic State group's blast killed nine journalists in April last year, including AFP Kabul's chief photographer Shah Marai.
It was the second time a Romanian national was killed by the Taliban this week. On Monday, a Romanian was among at least 16 people killed in a Taliban attack on a residential area in east Kabul.
- 'Bitten by the snake' -
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The capital has been gripped by a surge in deadly violence even after the US and the insurgents reached an agreement "in principle" that would see the Pentagon pull thousands of troops from Afghanistan in return for various Taliban security promises.
But there is increasing unease about the deal, which Afghans fear will lead to a return of the Islamist extremist Taliban to power.
A growing chorus of US lawmakers and officials are also expressing doubts.
On Thursday, the State Department said that the US negotiator, Zalmay Khalilzad, had returned to Qatar for further talks with the Taliban.
The deal still needs the approval of President Donald Trump, who has said that he wants to end American involvement launched after the September 11, 2001 attacks.
According to parts of the deal made public so far, the Pentagon would pull about 5,000 of its roughly 13,000 or so troops from five bases across Afghanistan by early next year.
The insurgents in turn will renounce Al-Qaeda, promise to fight the Islamic State group and stop jihadists using Afghanistan as a safe haven.
The Afghan government has expressed doubts about the prospective deal, saying officials need more information about the risks it poses.
"There is too much concern about it, and we are still not assured of what consequences this agreement could have for Afghanistan's future," presidential advisor Waheed Omar said Thursday.
"The people of Afghanistan have been bitten by the snake before, and have been witness to the consequences of hasty deals".
Afghan President Ashraf Ghani condemned the Taliban for "celebrating the deaths of innocent lives" after Thursday's attack.
In another gruesome moment in Afghanistan's war, Abdul Samad Amiri, the acting head of the country's independent human rights commission, was kidnapped and shot dead on Wednesday, allegedly by the Taliban.
Afghanistan's intelligence chief Mohammad Masoom Stanekzai, who has come under intense pressure over the violence, quit Thursday following a deadly raid in the east of the country in which security forces killed four brothers.