Spanta said relations between the neighbouring states, which in the past had deteriorated over responsibility for border attacks by fighters, had "remarkably improved".
Swat Sharia deal
International concerns have been raised over Pakistan's strategy for dealing with fighters after it reached a deal with religious leaders in the Swat valley near Islamabad to introduce Sharia or Islamic law as part of a truce.
On Tuesday, Taliban fighters in Pakistan declared an indefinite ceasefire in the Swat valley, the group's spokesman said.
Critics in the US, Europe, Afghanistan and India, have expressed concerns the move will embolden al-Qaeda and Taliban fighters in North West Frontier Province, which borders Afghanistan.
|Shah Mehmood Qureshi said the Swat
policy was a "local solution" [EPA]
The Taliban imposed a strict version of Sharia law during its 1996-2001 rule in Afghanistan.
Qureshi said the Swat policy represented a "local solution to a local problem" and was "not any appeasement toward militants".
"The Afghanistan government has confidence in the leadership in Pakistan," Spanta said after holding talks with Qureshi about the new policy.
US relations with Pakistan have also come under increasing scrutiny since Barack Obama, the US president, took office in January with some US politicians questioning the level of aid given to the country.
A US congressional report published on on Monday said Washington had spent $12.3bn since 2002 aiming to end the "terrorist threat" on Pakistan's border with Afghanistan.
The meetings in Washington following Obama's decision last week to send an additional 17,000 troops to Afghanistan to battle Taliban fighters, bringing US forces there to 55,000 by this summer.
That announcement came after the army said it was suspending operations in the troubled region.