Aziz, the national security and foreign affairs adviser to Pakistani Prime Minister Nawaz Sharif, met with Afghan Foreign Minister Zalmai Rassoul, The Wall Street Journal said.
Aziz pledged to adopt a policy of non-interference in Afghan affairs.
He also said Pakistan is willing to help with the Taliban talks.
"We have ... some contacts with the Taliban in the past, but we don't control them," Aziz said.
Rassoul said Aziz's visit marked a new chapter in the two country's relations, but he also said Pakistan's past efforts have not gone far enough.
The Afghan government has said it wants Pakistan to release Mullah Abdul Ghani Baradar, a former Taliban leader, as a confidence-building measure.
Although Pakistan has released some Taliban prisoners, Afghanistan has criticized the country for failing to do more.
"Unfortunately, so far, we haven't seen any concrete results from our efforts to improve relations with Pakistan, and to encourage Pakistan to support peace and reconciliation efforts," a senior Afghan official told the Journal.