Karzai has repeatedly accused the Pakistani government of failing to prevent fighters active in the tribal zone from entering Afghanistan.
He also warned Baitullah Mehsud, a Pakistan-based Taliban leader, that Afghan forces "will go after him now and hit him in his house".
He gave the same warning to Taliban leader Mullah Omar.
Yousuf Raza Gilani, the Pakistani prime minister, said Islamabad will not allow anyone to interfere in its internal affairs.
"We will neither interfere in the internal affairs of any country, nor will we allow anyone to interfere in our affairs," Gilani told private ARY-OneWorld television.
"Such statements will not help in the normalisation of friendly relations between the two countries and will hurt the sentiments of people on both sides of the border," Gilani said.
Al Jazeera's Kamal Hyder, reporting from Peshawar, said that Karzai's comments are likely to cause anger in Pakistan.
"When Karzai says his forces will go into Pakistan, this kind of talk will not go down well in Islamabad because Pakistan has already been complaining to Nato and US forces for violating the sovereignty of Pakistan," he said.
"We also have to remember the historcal context with respect to relations between the two countries, and they have now come to a very low point, and may further slide if Afghan forces enter Pakistani territory."
Meanwhile, more than 15 anti-government fighters have been killed in Afghanistan during the hunt for those who escaped from prison after a Taliban attack, US-led forces said.
|Pakistanis are angry at alleged Nato and |
US violation of their sovereignty [AFP]
Afghan and international troops have been searching for more than 1,100 inmates who fled after the Taliban blasted open a prison in the southern city of Kandahar on Friday.
During the search, air strikes were called in west of Rawonay, Kandahar province, to destroy a farming compound, the US-led forces said in a statement on Sunday.
Five people were also captured but it has not been confirmed if those killed or detained had been prisoners from the Kandahar jail.
"A large cache of munitions and IED components were discovered during the search," the statement said.
"The combined forces used precision air strikes to destroy the compound after insurgents attacked with small-arms fire."
Sayed Agha Saqib, Kandahar's police chief, said that 14 people who broke out of the prison had been recaptured.
Six others were taken back into custody on Saturday.
The Taliban said 400 of its own fighters had escaped in the prison attack, which they said had been planned over two months.
Afghan authorities put the number of prisoners who fled at 886, of whom more than 380 were Taliban fighters.
Nato's International Security Assistance Force (Isaf), which is separate from the US-led forces, said more than 1,100 prisoners had escaped.
Afghan authorities have launched an investigation to find out if any government officials were involved in the jailbreak which began when a suicide bomber drove a truck loaded with bombs into the jail gate and blew it up.
Several dozen Taliban fighters, armed with rocket-propelled grenades and rifles, then stormed the mud-built compound and freed the prisoners.
A Taliban spokesman said all Taliban prisoners had reached "safe destinations".
Separately, US-led forces killed several fighters in ground and air strikes in the Garmser district of the neighbouring Helmand province on Saturday, the US military said.