Gilani denied rumours that Zardari had suffered a stroke and that the army was trying to push him out of office.
He said Zardari, who is being treated for a heart condition in Dubai, was improving rapidly and that his medical tests were clear.
But the President would need two weeks’ rest before returning home, Gilani told BBC in an interview.
Gilani further denied that the President had written a letter of resignation, as claimed by a source in Dubai.
“Why should he write (a letter of resignation)?” asked Gilani.” He has the backing and support of the entire parliament.” Dismissing speculation about a “quiet coup”, the premier said: “Rumours are rumours”.
Zardari’s abrupt departure for Dubai last week and contradictory statements from government officials about his health has led to speculation that the unpopular President might resign due to growing pressure on him from the powerful military.
The President has been at the centre of a storm since Pakistani-American businessman Mansoor Ijaz made public a secret memorandum sent to the US military that sought American help to stave off a possible military takeover in May.
Despite denials from officials, Islamabad continues to be abuzz with rumours that Zardari had suffered a “minor heart attack”.
Gulf News daily has quoted an unnamed presidential aide as saying that Zardari may not return to Pakistan from Dubai for weeks.
Leaders of the Pakistan People’s Party-led government, including Gilani, have stepped in to defend the President.
They have insisted that Zardari’s condition has improved and that he will return to the country soon.