Some 300 people also protested against the shelling in Asadabad, the capital of eastern Kunar province, demanding an end to the shelling and calling for revenge.
Hundreds of rockets have hit Afghanistan since early June, officials say, and killed dozens of civilians, infuriating Afghans from ordinary villagers to the top echelons of power.
A top Afghan police general last week offered his resignation over the government's response to the attacks, and there have been at least two demonstrations
Karzai said his Interior and Defence Ministers had sought permission to open fire if more rockets landed.
But the president said he had refused because returning fire risked creating more innocent victims in Pakistan.
"Afghanistan never wants to harm civilians in Pakistan with its response," Karzai told a joint news conference in Kabul with visiting British Prime Minister David Cameron.
"Afghanistan is seriously engaged in talks with Pakistan to solve this issue," he added.
Karzai's parliament, despite facing internal turmoil after a government-backed court ruled in June to unseat 62 lawmakers, has focused debate on the attacks for the last three days, and wants to see sterner action.
"The parliamentarians called on the government to cut ties with Pakistan because its non-stop shells have killed many innocent civilians," said Fraidoon Momand, a lawmaker from eastern Nangarhar province, which has been hit.
"We have long demanded that Pakistan explain the shelling but they didn't," he added.
Displaced, injured, dead
The Interior Ministry says nearly 800 rockets have been fired since early June, killing 12 women and girls and 30 men.
Some 55 have been wounded, and 120 houses destroyed.
Pakistan last Monday rejected Afghan allegations of large scale cross-border shelling, saying that only "a few accidental rounds" may have crossed the border when it pursued militants who had attacked its security forces.
It is impossible to verify independently exactly what is happening on the remote, porous and disputed mountainous border, but there are insurgent groups on both sides.
Pakistan has in the past fiercely contested cross-border attacks by NATO forces chasing insurgents on its territory.
Fazlullah Wahidi, the governor of Kunar province, said 635 rockets had been fired into Kunar province killing 22 people and wounding 40. Local people said they would take revenge if they could find weapons.
"My weapon was taken by foreign troops long ago. Now how can I defend my people from brutal rockets from Pakistan," said protester Ahmad Khan.
"If the NATO forces cannot protect us, they should give back our weapons so we could revenge our people."
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