The court's order is the latest twist in the legal tussle between the Supreme Court and the prime minister's office -- in this case a new prime minister -- over the corruption allegations against Zardari.
Ashraf owes his job to the refusal by the last prime minister -- Syed Yousuf Raza Gilani -- to follow up on corruption allegations against Zardari, claiming as president Zardari was immune from prosecution.
The Supreme Court disagreed and convicted Gilani, 60, of contempt of court, which meant he couldn't hold office and Parliament had to vote last week to appoint a new prime minister.
Ashraf won the vote, gaining 211 votes in the 342-seat Parliament and took office only to find himself in the same hot seat as did Gilani.
Ashraf, 62, immediately went on the offensive after assuming office.
In his inaugural speech is warned against forces trying to undermine the supremacy of Parliament and vowed to hold free and fair elections when they are due next year, a report by the Associated Press of Pakistan said last week.
But the Supreme Court said this week in a brief order that it expected Ashraf to act on the court's directives.
The attorney general also has been ordered to consult with Ashraf about how to proceed, the court statement said.
All three men are members of the ruling Pakistan Peoples Party, another issue the Supreme Court is having to pass judgment upon.
This week the Lahore High Court ordered Zardari to relinquish his post as co-chairman of the PPP before Sept. 5, otherwise be in contempt of court, DawnNews reported.
The court has been hearing petitions against the president for holding dual posts.
Chief Justice Justice Umar Atta Bandial of the Lahore High court and head of the three judge bench, said court had provided the president with enough time to resign from his post as the co-chairman of the PPP and suspend all political activities in the presidency before Sept. 5.
Ashraf also is having to fight corruption charges from when he was water and power minister and introduced the controversial Rental Power Plants scheme.
The scheme involved private companies setting up small temporary power generation plants that could run during times of peak energy consumption, a plan to avoid power shortages and outages.
But in March 2011, the Supreme Court declared the Rental Power Plants scheme illegal and all RPPs were ordered to shut down immediately.
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