Brader's fate and what role Pakistan plays in any peace effort are among the many subjects that Karzai is expected to discuss with high-level Pakistani officials during his visit.
"We in Afghanistan are fully aware and recognise that without Pakistan and without its co-operation with Afghanistan, Afghanistan cannot be stable or peaceful," Karzai said after talks with Yousuf Raza Gilani, the Pakistani prime minister, on Thursday.
"It is also, I believe, recognised in Pakistan that without a stable and peaceful Afghanistan there cannot be stability or peace in Pakistan.
"Afghanistan does not want any proxy wars on its territory. It does not want a proxy war between India and Pakistan on Afghanistan.
"It does not want a proxy war between Iran and the United States on Afghanistan. It does not want any country ... to engage in any activity against another country in Afghanistan."
Karzai, who met his Pakistan counterpart Asif Ali Zardari on Wednesday, said Kabul is not as far ahead on reconciliation plans as some have speculated, but that it was committed to the process.
He said his government had contacts within the Taliban leadership "as high as you wish to go", but would not say if that included Mullah Omar.
He reiterated his willingness to talk to Mullah Omar "as an Afghan to Afghan".
Al Jazeera's Hashem Ahelbarra, reporting from Islamabad, said there is a sense of shift in rhetoric.
"We are seeing a radical change in the rhetoric with both sides saying they are suffering the same problems," he said.
"They seem to be sending a message to the international community that a military option is not the best solution, that instead they would like to see international assistance trickling into tribal areas."
Britain has urged Pakistan to push ahead in the peace process.
The US has been more cautious in supporting a peace plan and has instead preferred to highlight programmes focusing on reintegrating disaffected Taliban fighters into broader Afghan society.
Pakistan has made it clear it wants a part in so-called reconciliation efforts between the Taliban and the Afghan government.
Many Afghans resent Pakistan's involvement in their affairs, but Pakistan's history of links to the Afghan Taliban, a group it supported when the group controlled Afghanistan in the 1990s, could make Islamabad an indispensable player.
Deadly missile attacks
Karzai's visit to Islamabad coincided with reports of deaths of up to 16 suspected fighters in two US missile attacks in Pakistan's northwest tribal belt.
Two successive bombing raids by unmanned spy planes hit a building and vehicles late on Wednesday in North Waziristan, a hub of Taliban and al-Qaeda-linked fighters near Pakistan's border with Afghanistan.
Pakistani security officials said more bodies were recovered from the wreckage on Thursday. At least five of those killed were foreign fighters, a senior security official in the region said.
Seven fighters were killed in the first raid targeting a compound and a nearby vehicle in Mizar Madakhel village, about 50km west of Miranshah, the main town in North Waziristan.
Nine more fighters died in a second attack, which hit shortly after as they pulled bodies from the rubble of the first bombing raid.