The spokesman, Humayun Hamidzada, did not name Pakistan's intelligence agency but told reporters it was "pretty obvious" who was behind Monday's bombing, which killed 41 people and wounded 150.
An Afghan security report released earlier Tuesday found that the bombing could not have succeeded without the support of foreign intelligence agencies, another reference to Pakistan, India's archrival.
"The sophistication of this attack, and the kind of material that was used and the specific targeting, everything has the hallmark of a particular intelligence agency that has conducted similar attacks inside Afghanistan in the past. We have sufficient evidence to say that," Hamidzada said. "The project was designed outside Afghanistan. It was exported to Afghanistan."
Among the blast's victims were four Indians working in the embassy, including the military attache and a diplomat.
Pakistan's prime minister denied Tuesday that its intelligence service was behind the attack. Speaking in Malaysia, Syed Yousuf Raza Gilani said his country has no interest in destabilizing Afghanistan when both countries are fighting terrorism.
"We want stability in the region. We ourselves are a victim of terrorism and extremism," said Gilani on the sidelines of a summit of eight developing Islamic nations. He did not elaborate.
Pakistani Foreign Minister Makhdoom Shah Mahmood condemned the attack on Monday, but Gilani's comment is the first high-level denial of involvement by the government.
Also on Tuesday, Afghanistan summoned the charge d'affair of the Pakistan Embassy to Afghanistan's Foreign Ministry over comments made by a former Pakistan member of parliament mentioning the need for jihad against U.S. and NATO forces in Afghanistan.
Afghanistan often accuses Pakistani intelligence of supporting the Taliban insurgency, a charge denied by Islamabad.
The bodies of the four Indians killed in the attack were flown back home late Monday aboard an Indian military plane, said Gen. Ahmad Zia Aftali, the head of Kabul's main military hospital.
Senior Afghan government officials were at the airport, including Defense Minister Abdul Rahim Wardak and President Hamid Karzai's national security adviser Zalmay Rasoul, Aftali said.
Karzai condemned the bombing Monday and said it was carried out by militants trying to rupture the Afghan-India friendship. He told the Indian prime minister during a phone conversation that Afghanistan would do all it could do identify the attackers.
The blast was the deadliest in Kabul since the fall of the Taliban in 2001.
Suspicion of Pakistan's involvement runs deep in the U.S.-backed government in Afghanistan - Pakistani intelligence helped create the Taliban militia, many of whose leaders and recruits studied at religious schools in Pakistan.
Despite international condemnation of the Taliban regime's fundamentalist rule in Afghanistan from 1996-2001, Pakistan was one of the few countries that gave it diplomatic recognition.
Pakistan formally abandoned its support for the Taliban after Sept. 11 attacks on New York and Washington. Still, Taliban leaders are suspected of getting continued shelter and support in Pakistan, and maintaining links with the Pakistani intelligence agency.
Meanwhile, Pakistan views with suspicion the involvement of its longtime rival India in post-Taliban Afghanistan.
India has donated millions of dollars to Afghanistan for reconstruction, and there are thousands of Indian engineers and laborers in the country helping to build roads and other infrastructure.
Pakistanis are wary of Indian consulates established in the outlying cities of Kandahar, Jalalabad, Herat, and Mazar-i-Sharif. But Indian officials say they are there to support reconstruction. Militants have frequently attacked Indian offices and projects around Afghanistan.
Ikram Sehgal, a political analyst in Pakistan, said he doubted Pakistan's intelligence service was behind the attack. He said a more likely culprit is the Pashtuns - the largest of Afghan ethnic groups that also forms the core of the Taliban insurgency - saying they see the Indians as "enemies."