KABUL, Afghanistan – Pakistan's army chief made a surprise visit to Afghanistan Tuesday for border security talks with NATO and Afghan commanders, just a day after Pakistani President Pervez Musharraf announced his resignation.

Gen. Ashfaq Parvez Kayani spoke with President Hamid Karzai over the phone in Kabul on Tuesday, three officials told The Associated Press. Kayani's visit was striking in that even Afghanistan's top leadership did not know he was coming, officials said.

But Pakistan's military spokesman, Maj. Gen. Athar Abbas said the trip was scheduled at least a month and a half ago and was part of a series of tripartite meetings designed to underpin cross-border cooperation against insurgents.

Earlier Tuesday, Karzai, in his first public response to Musharraf's resignation, appealed for a fresh approach to what has often been a troubled relationship between the two neighbors.

“I wish President Musharraf all the best. We have had difficult days together, but also we had good days together. All in all, we had a good relationship,” Karzai told the AP in an interview.

“The most important thing . . . is not personalities. What is important is that we change our expectations and the way we formulate policies to meet those expectations,” he said.

Karzai has been a strident critic of sanctuaries within Pakistan where he says insurgent Taliban and other militants regroup, rearm and train to fight in Afghanistan.

Karzai stopped short of accusing Pakistan of official support for the insurgency but said, “If they are doing that in order to get strategic depth, it will not happen. It has been tried before. It failed. If they are doing that in order to have a puppet government, it will not happen, it will not work.

“If they are doing that to gain an upper hand against another of their neighbors,” Karzai said in a reference to Pakistan's hostile relationship with India, “it won't happen.”

The Pakistan military said Kayani met with the commander of NATO forces in Afghanistan, Gen. David McKiernan, and Gen. Bismullah Khan, the head of the Afghan National Army.

The generals reviewed security along the border and were satisfied “at the existing level of cooperation,” the military said in a statement. They also reiterated their commitment to help bring peace to the region, it said.

Kayani took over as army chief last year when Musharraf quit the post to become a civilian president, significantly reducing his influence in Pakistani politics.

Musharraf was Washington's key ally in the fight against insurgents on the Afghan-Pakistan border, although the strength of the insurgents on both sides of the border increased substantially during his term as army chief. An agreement he signed with insurgents in 2006 is often cited as giving room to al-Qaeda to regroup in Pakistan's South Waziristan tribal region.

Musharraf's resignation, however, puts pressure on Pakistan's newly elected government to provide new leadership in the country's fight against militants.

McKiernan, the NATO commander in Afghanistan, told the AP in an interview Monday that a troubling trend is occurring in the border regions, with increased training, easier cross-border movement and an increase in militants fighters coming to the region from Central Asia, the Middle East and “even some Europeans.”

Associated Press writers Jason Straziuso and Amir Shah contributed to this report from Kabul.