The Afghan leader met the visiting adviser to the Pakistani Prime Minister on national security and foreign affairs Sartaj Aziz late Sunday, reports Xinhua.
Aziz delivered the official invitation of Prime Minister Nawaz Sharif to President Karzai.
"Karzai agreed in principle to visit Pakistan but insisted that the Afghan delegation will not visit Pakistan unless the agenda includes the Afghan peace process and serious and effective campaign against terrorism," the Khama press website reported.
The visit of Aziz is the first high-level exchange between the two countries since the assumption of new government in Pakistan following the May 11 election.
The visit is seen as an important step to push for the stalled Afghan peace talks with the Taliban.
Aziz also met with Afghan Foreign Minister Zualmai Rasoul Sunday, reiterating Islamabad's support for "Afghan-led" peace and reconciliation process, the report said.
"For us, a peaceful, stable and united Afghanistan is in the interest of Pakistan," Aziz said, calling for a "close relationship" with Afghanistan.