Karzai is the first head of state to visit Pakistan since US Navy Seals killed Al-Qaeda chief Osama bin Laden on Pakistani soil, increasing pressure in the US for a peace deal in Afghanistan.
He meets Zardari on Friday and Gilani on Saturday. A joint peace commission involving officials from both countries is also set to meet.
Afghan officials say that contacts with the Taliban are now “systematic” and the US is pressing the UN to lift sanctions on 18 former senior Taliban figures, some of whom could act as go-betweens, according to the UK’s Guardian newspaper.
Pakistan officially says that peace efforts are an Afghan affair. But its secret services, the Inter Services Intelligence (ISI), are widely believed to view the Afghan Taliban and the Haqqani network as a foreign policy tool, even if the bin Laden killing may have undermined that relationship.
Karzai is likely to seek reassurances that Pakistan will not hinder an agreement. The US is also insisting that a deal commits Islamabad not to provide safe haven for Taliban or other insurgents on its territory.
Pakistan may be more amenable due to the activity of its own home-grown Tehreek-e-Taliban, although it is worried about the growing influence of its longstanding enemy, India, in Afghanistan.
But there is no guarantee that the Pakistani state will speak with one voice. Even if the powerful army chief Ashfaq Kayani recently met Karzai, apparently to get rid of bad blood, some of the lower ranks are clearly committed to an Islamist agenda and not all of the ISI may agree with the politicians' definition of the national interest.
A suicide bomber killed four police officers and injured 18 other people in an attack on the funeral of the assassinated police chief Mohammed Daoud Daoud.
Officials say that police prevented the bomber entering the mosque where prayers for Daoud were being held. They believe that his main target was the provincial police chief, who was not hurt.