The bomb was planted in a rickshaw.
The explosion killed at least 150 people and wounded more than 450.
On the same day, a rocket struck the Indian diplomatic compound in Kabul.
Neither Haqqani Network - Taliban-affiliated group - nor Daesh claimed responsibility.
Meanwhile, Afghan President Ashraf Ghani issued an ultimatum to the Taliban Tuesday, warning them to embrace peace or "face consequences" after announcing that the death toll from last week's truck bombing had passed 150.
At the same time that last Wednesday's attack occurred, the Trump administration was trying to decide whether to send another 5,000 or so American troops there to bolster the Afghan forces' shaky efforts to defend the country from the Taliban and other resistance to the rule of President Ashraf Ghani and his government.
Mr Ghani's government has faced protests for failing to tackle the deteriorating security situation.
Under Obama, the USA supported peace deals that Ghani's government made with former warlords, such as Gulbuddin Hekmatyar, and White House officials admitted a resolution to Afghanistan's conflict will require a truce with the Taliban.
The developments come as the two nations have also engaged in a series of deadly cross-border clashes this year.
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When asked by the authorities about his intentions, Zaghba initially replied that he was leaving to become "a terrorist". But he successfully got them back after a court determined there wasn't enough evidence to arrest him.
Almost a week after the explosion, no group has claimed to have carried out the attack.
Ghani also renewed his criticism of neighboring Pakistan, saying it was waging an "undeclared war of aggression" against his country. "What we need is an agreement on regional security", he said.
He said Afghanistan had offered Pakistan a vision of prosperity by linking south and central Asia through trade, investment and peaceful co-existence; however, he alleged Pakistan still believes it could sponsor and use terror as a controllable tool that can be switched on-and-off to suit its goals in the country.
This is not the first attempt by the Afghan government to broker peace.
The current global force in Afghanistan numbers about 13,000, about 8,400 of them are American, mostly tasked with training and advising the Afghan forces.
Before the bombings and the street demonstrations, the Trump administration was discussing whether to send another 3,000-5,000 U.S. troops to Afghanistan, but now that will hardly be sufficient.
U.S. Charge d'Affaires Hugo Llorens, who is overseeing the American embassy as no new ambassador has been nominated by Trump, said the conference was a chance to send the message that "the enemies of Afghanistan can not win".
The Afghan intelligence service, the National Directorate of Security (NDS), said on Thursday that early findings showed the Haqqani network with the assistance of Pakistan's ISI carried out the attack in Kabul that killed at least 90 people.
Ghani reiterated on Tuesday that he wants peace talks with the Taliban, but said that it wasn't an "open-ended" opportunity.
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