Pakistan is seen as a critical regional player with the clout to help all parties in the conflict reach a settlement.
Karzai will meet President Asif Ali Zardari and other Pakistani leaders, although no breakthroughs are expected.
Aside from efforts to try to get the Taliban to lay down their arms, the two leaders are likely to discuss how al Qaeda leader Osama bin Laden's death could change the dynamics of a region where he has inspired militants for years.
Ties between Pakistan and Afghanistan have been hampered by mistrust.
Both Afghanistan and the United States say Pakistan is not doing enough to prevent militants from crossing the border to attack American-led NATO troops and Afghan security forces.
Pakistan says it is already stretched fighting its own home grown Taliban militants.
Analysts say it is reluctant because it sees some pro-Taliban militant groups like the Haqqani network as a counterweight to growing Indian influence in Afghanistan.
But Islamabad may be more inclined to act after the United States -- the source of billions of dollars in aid – discovered bin Laden had been living in Pakistan.
Pakistan, which backed the Taliban government that ruled Afghanistan during the 1990s, will be crucial to any attempts to stabilise its western neighbour.
Its intelligence services are still believed to have close links with many of the insurgent groups they funded and supported during the war against the Soviet Union and beyond, including the Taliban leadership which is based around the Pakistani city of Quetta.
Many lower level insurgents also find safe haven in Pakistan's lawless tribal regions. Pakistan has often been accused of playing a "double game", promising the United States it will go after militants while still supporting some of them, an allegation it denies.
Nevertheless it is seen as an important ally to the United States and other NATO members as they seek to bring the Taliban to the negotiating table.
"As far as Pakistan is concerned, we categorically said that Pakistan wants a peaceful, stable Afghanistan and we are ready to facilitate any Afghan-led, Afghan-owned process of reconciliation and peace," said foreign ministry spokeswoman Tehmina Janjua.
Pakistani and Afghan military and intelligence chiefs and other officials -- part of a joint commission on reconciliation and peace -- are due to hold their first formal talks as part of Karzai's visit.
This summer foreign forces will hand security control in parts of Afghanistan to the national police and army, launching a nearly four-year long process that Western nations and Karzai hope will ensure the departure of all international combat troops by the end of 2014.
US Defense Secretary Robert Gates said this month that there could be political talks with the Afghan Taliban by the end of this year if NATO made more military advances and applied pressure on the insurgents.
He has also stressed there would be no hasty US troop withdrawal from Afghanistan and Washington expected the same from its allies.
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