On Wednesday, the Taliban denied responsibility and said they condemned attacks that killed civilians.
Also in the area is Afghanistan's foreign ministry, the presidential palace and its intelligence and security headquarters, guarded by soldiers trained by the United States and its coalition partners.
One local shop owner, Sayed Rahman, told Reuters his store was badly damaged, adding: "I have never seen such a bad explosion in my life".
US President Trump called Afghanistan's President Ashraf Ghani to convey his condolences, saying the timing of the attack during the holy month of Ramadan underscores "the barbaric nature of the terrorists who are enemies of all civilised peoples".
'It felt like an natural disaster, ' said 21-year-old Mohammad Hassan, describing the moment the blast struck the bank where he was working.
Afghan troops are backed by U.S. and North Atlantic Treaty Organisation forces, and the White House is considering sending thousands more soldiers to break the deadlock in the battle against the Taliban.
There are now 8,500 US troops in Afghanistan with a USA promise of more to come.
Germany considers areas of Afghanistan, including Kabul, safe and has been regularly deporting Afghans whose asylum requests have been rejected, particularly those with criminal records.
Afghanistan Thursday mourned the victims of a massive truck bomb that blew up Wednesday in the diplomatic section of the country's capital, killing at least 90 people and wounding more than 400 others.
Pajhwok news agency quoted Najib Danish of the Ministry of Interior as saying that it was a suicide vehicle bombing.
A day after a ghastly suicide bomb attack in Kabul claimed the lives of at least 90 people and injured scores others, Afghanistan has cancelled all proposed home and away cricket fixtures with Pakistan, blaming the attack on militants backed by Islamabad.
Mohammad Sarwar stood crying behind the gate of an emergency hospital, looking for his nephew, Habibullah, who was missing.
Foreign Ministry spokesperson Nafees Zakaria said such accusations will only hinder the peace process. Casualties and injuries were reported only from the German embassy, with an Afghan security guard among the dead and some staffers injured.
"Not just the US, NATO has put billions of dollars into training and reorganizing the Afghan army". "It used to be that Kabul was this island of security. now we're seeing (violence) penetrate the capital".
"Four BBC journalists were also injured and were treated in hospital".
"The indications are that (Wednesday's attack) was carried out by terrorists outside Afghanistan".