Pakistani officials said Zardari, 56, flew to the United Arab Emirates on December 6 after falling ill.
A spokesmen for the president denied that Zardari was planning to step down and said his condition was stable and that examinations by doctors were continuing.
There has been no official confirmation from the president's office of reports that Zardari had suffered a minor heart attack.
In Washington, State Department spokesman Mark Toner said the United States believes that Zardari's travel was linked to a heart condition and wished him a speedy recovery.
Asked about speculation it could be linked to a military takeover of Pakistan, Toner told reporters that U.S. officials believe the case is "completely health-related."
Reports say Zardari, who became president in 2008, has been facing pressure from Pakistan's powerful military since the Pakistani ambassador to the United States was forced to resign over allegations he sent a memo to the U.S. government asking for help to restrain the military.
compiled from agency reports