Zardari left for the US shortly after midnight to attend the NATO Summit in Chicago during May 20-21.
Pakistani officials have said Zardari was extended an unconditional invitation by NATO Secretary General Anders Fogh Rasmussen though analysts believe the move was linked to Islamabad`s decision to move towards reopening the supply routes.
The President will address the expanded International Security Assistance Force meeting of NATO and meet various heads of state and government on the margins of the summit.
Foreign Minister Hina Rabbani Khar and Foreign Secretary Jalil Abbas Jillani are part of the President`s delegation.
Over the past few days, Pakistani and American officials have been engaged in hectic negotiations on a deal to reopen the NATO supply routes, which were closed in November after a cross-border air strike by US forces in Afghanistan killed 24 Pakistani soldiers.
Efforts to reopen the supply lines were held up by Pakistan`s insistence on an unconditional apology and an end to US drone strikes. Diplomatic sources told PTI that the deal on the supply routes hinged on negotiations on some crucial issues, including the fee to be paid to Pakistan for every NATO container and tanker passing through its territory and security for supply convoys.
Though reports in the Western media have said Pakistan has demanded between USD 1,500 and 5,000 for every container, the sources, who were familiar with the negotiations, said the US was would be agreeable to paying about USD 500 dollars to USD 700 for every container.
Some reports have suggested that a levy of about USD 1,500 per container would increase the cost of the US-led war effort in Afghanistan by about a million dollars a day or USD 365 million a year. The sources said a deal is expected to be finalised soon so that the supply routes can be reopened next week.