This was conveyed during a telephonic conversation between Afghan President Ashraf Ghani and Pakistan Army chief General Raheel Sharif, Dawn online quoted a security source as saying.
According to the source, Pakistan has sought more evidence from the Afghan side over the attack.
Ghani had called Raheel Sharif and demanded that action be taken against the attackers' accomplices.
The conversation took place as US Special Envoy for Afghanistan and Pakistan Richard Olson, Special Assistant to the US President Peter Lavoy and Commander of Resolute Support Mission in Afghanistan General John Nicholson visited Islamabad and held meetings at the General Headquarters and Foreign Office.
At least 12 people were killed and 45 injured in the attack on American University in Kabul on Wednesday evening that continued for over 10 hours.
The Afghan government shared three mobile numbers operating in Pakistan, which it claimed had remained in contact with the attackers. Subsequently, the Pakistan Army initiated a combing operation along the Pak-Afghan border near Chaman to find the suspects.
"We searched, but no-one was found during the operation," the source said.
The ISPR in a statement said: "Our evaluation of the evidence provided and outcome of combing operation so far, has shown that all Afghan SIMs used during the attack were from a network owned and operated by an Afghan company whose spillover signal affects some areas along the Pak-Afghan border."
Sharif assured Ghani of "all-out cooperation" in investigating the role of Pakistan-based elements in the attack, but stressed that it could happen only after Afghans provide "more information".
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