"Our thoughts are with the families of the deceased & prayers with the injured", he tweeted.
The US embassy and the North Atlantic Treaty Organisation mission are about half a mile from the site. They're now one of the biggest contributors to the NATO-led Resolute Support mission with around 980 soldiers on the ground to support and train Afghan security forces.
Authorities in Germany postponed a deportation flight due to return failed Afghan asylum seekers, with a government source telling newsmen that diplomatic and consular staff had "more important things to do than to deal with organisational matters" so soon after the attack.
Freeland says all embassy employees are safe.
The German embassy was heavily damaged, but the Washington Post reports that it's unclear if the building was targeted. No one has claimed responsibility for the explosion, but the Afghan intelligence service NDS said in a statement that their initial findings pointed to the Haqqani network as being responsible for the attack. The Chinese, Turkish and Iranian embassies are also located there.
Bystanders lifted an injured man from the back of a pickup as others hovered nearby in bloody clothes, some pressing pieces of cloth to their wounds. The BBC said one of its drivers, an Afghan, was killed driving journalists to work.
People at site of huge blast that killed at least 80 people describe scenes of confusion and large-scale destruction.
Most of the casualties were Afghans but foreign nationals were also injured, including 11 USA citizens.More news: Modi, Putin summit: All eyes on nuclear power deal
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The attack came as the Taliban steps up their annual "spring offensive".
The explosives were hidden in a tanker truck used to clean out septic systems, according to Najib Danish, deputy spokesman for the interior minister. His statement added that the Taliban condemn "every explosion and attack carried out against civilians, or in which civilians are harmed".
"We pray for a speedy recovery to the American and Afghan members of our mission staff and others who were injured in this attack, and we praise the Afghan Security Forces, police, and medical professionals who were the first responders to the scene", Tillerson said.
WATCH: Security and emergency services rushed on Wednesday to the site of a massive vehicle bomb in Afghanistan's capital, which authorities say killed at least 80 people. Abdullah Habibzai said an initial estimate put the total damage from the bombing at 1 billion Afghanis ($1.5 million), but said that number could rise.
There was no claim of responsibility.
The neighbourhood is considered Kabul's safest area, with foreign embassies protected by dozens of 10-foot-high blast walls and government offices, guarded by police and national security forces.
German Foreign Minister Sigmar Gabriel said the "despicable" attack had happened "in the immediate vicinity" of the German embassy and that an Afghan guard had also been killed.