Wednesday's attack close to the heavily protected diplomatic area killed about 90 people and injured about 350 others.
No group has said it carried out the attack, but Afghan intelligence officials suggested the Haqqani network - militants allied with the Taliban - carried it out with Pakistan's support.
Pakistan's foreign ministry spokesman described the claim as baseless.
Stability in Afghanistan was in Pakistan's interests, said Nafees Zakaria, and the "rhetoric of blaming others" to hide Afghanistan's own failures was unhelpful.
Pakistan and Afghanistan frequently accuse each other of supporting and harbouring militants who carry out cross-border attacks. Afghanistan on Wednesday cancelled all planned cricket fixtures with Pakistan in response to the blast.
The Taliban has denied any role in the attack. There has been no comment from so-called Islamic State (IS), which has a small presence in eastern Afghanistan and has been quick to claim attacks in recent months.
Wednesday's attack was one of the deadliest in Kabul in recent years. A tanker truck packed with explosives was detonated close to the German embassy near Zanbaq Square at 08:20 local time (03:50 GMT).
The bomb's target is unknown but many of those who died in what witnesses described as a massive explosion were Afghan civilians. Mohammed Nazir, a driver for BBC Afghan, died in the blast.
Buildings, including a number of embassies, were damaged and more than 50 vehicles destroyed.
On Thursday relatives of people who have been missing since the attack were searching hospitals in the capital.
"I do not know if my son is dead or alive. I have to see and find him," one relative, Besmillah, told Reuters news agency outside the Emergency Hospital. "I went to every single hospital but could not find my son."
There have been several high-profile attacks in Kabul and around the country in recent months. Some people have been hitting out at the government for not doing enough to stop them.
"I have lost my brother in the blast and the government is constantly failing to provide us with security," AFP news agency quoted one resident as saying.
The Afghan interior minister has suspended four police officers over the blast, including the sheriff in charge of policing the diplomatic enclave and the head of the regional counter-terrorism department.
The blast has been condemned around the world. US President Donald Trump called Afghan leader Ashraf Ghani to express condolences.
The US has about 8,400 troops in Afghanistan, with another 5,000 from Nato allies.
The Pentagon has reportedly pressed Mr Trump to send thousands more troops back to try to counter gains by the Taliban. More than a third of Afghanistan is now said to be outside government control.
Early on Thursday a soldier died when a suicide bomber targeted a security checkpoint near the airport in Jalalabad.
Pakistan has rejected an Afghan claim that it was involved in a massive bomb attack in the capital, Kabul.