"Attacks such as these only serve to strengthen our commitment to our Afghan partners as they seek a peaceful, stable future for their country", North Atlantic Treaty Organisation said in the statement.
China's foreign ministry said its embassy was partly damaged but that no staffers or Chinese citizens were injured.
This is rapidly becoming one of the deadliest attacks in Afghanistan throughout the war.
"None of their injuries appear to be life-threatening".
The NDS further said that the attack was carried out with the support of Inter Services Intelligence (ISI), the Pakistani military intelligence.
Pakistan and Afghanistan have often traded accusations that each side harbors militants who stage attacks in the other country.
Afghan security forces and residents stand near the crater left by a truck bomb attack in Kabul on May 31, 2017.
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The Australian embassy was put into lockdown but a Defence Department spokesman said all Australian personnel deployed to Afghanistan had been accounted for. ISIS claimed responsibility for that attack. "Our thoughts are with the families of the deceased & prayers with the injured". "I wish the injured the speediest possible recovery", the telegram of condolences reads.
Indian Prime Minister Narendra Modi also denounced the attack on Twitter and expressed solidarity with Afghanistan in combating terrorism.
The truck, believed to be driven by a suicide bomber, exploded with a deafening roar at 8:22 a.m.in downtown Kabul when the roads were packed with motorists driving to work, the Afghan media reported. The Wazir Akbar Khan district is home to most of the capital's foreign embassies as well as several major government institutions, including the Presidential Palace.
At least 11 Afghan guards working for the U.S. embassy were among those killed and 11 American citizens working as contractors in Kabul were among the wounded, USA officials have said.
Ismail Kawasi says it was not immediately known what the target of the attack was on Wednesday morning.
As of late Wednesday night in Kabul, no one had claimed responsibility.
The US Embassy said "a large vehicle borne improvised explosive device" detonated near the southern edge of the diplomatic area.
Talking exclusively to India Today, Afghanistan Interior Ministry spokesperson Sediq Siddiqui said role of Pakistan's ISI has been established in Kabul explosion. Almost two hours after the explosion near Zanbaq Square, a crowded area in the capital that leads to the presidential palace as well as major foreign embassies, plumes of smoke were still rising from the scene.
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