Zardari became leader of the Pakistan's Peoples Party along with their son Bilawal after Bhutto's assassination on December 27.
He is now trying to put together a coalition after the PPP won most seats in elections this week.
At a hearing on Wednesday, Swiss lawyers for Pakistan argued that money-laundering charges against Zardari should proceed in Geneva despite Pervez Musharraf, the Pakistani president, dropping all graft charges against the couple last year.
The constitutionality of the amnesty has not yet been ratified by the supreme court in Pakistan.
The Swiss lawyers said the decision was expected in "a few weeks".
Dominique Henchoz, Pakistan's Swiss lawyer, told the Geneva court: "This dossier is a bomb for Zardari.
"His name appears on each page as the beneficial owner of offshore companies. Some 60 million Swiss francs have been frozen [in Geneva accounts."
The three-judge court in Geneva, presided over by Judge Valerie Laemmel-Julliard, said it would rule soon on whether to send the case to the prosecutor for trial, or back to a magistrate for more work.
Jacques Python, the senior lawyer for Pakistan, which is a civil party in the case, said: "The facts which Mr. Zardari stands accused of, taking commissions paid into accounts, are duly documented. It is urgent to act. The statute of limitations on some of the charges expires in July 2009."
Bhutto and Zardari have always denied the charges.
Saverio Lembo, Zardari's lawyer in Geneva, said that the case should be suspended until a decision on the amnesty is made.
The amnesty covers pending money-laundering cases in Switzerland and the UK.
Lembo told the court: "The case [in Pakistan] is going nowhere. There has been no ruling in 10 years. Why? The answer is simple - because this is all political."
Daniel Zappelli, the chief prosecutor, agreed that the supreme court ruling should come before any Swiss prosecution.
He said: "It's important to know whether or not the state of Pakistan believes its interests have been damaged.
"I await the position of Pakistan and to know whether it intends to pursue the criminal acts which it accuses Mr Zardari of."
In 2003, a Geneva court convicted Bhutto and Zardari of laundering funds linked to alleged kickbacks worth $13m.
However, the verdict was thrown out on appeal and a new investigation by magistrates was dismissed last October.
Charges against Bhutto ended when she was assassinated.
Zardari spent 11 years in jail in Pakistan on graft and other charges, none of which were proved.
Money laundering allegations would be harder to prove under Swiss law if the amnesty is upheld and corruption charges are dropped in Pakistan, legal experts say.
A Swiss conviction for aggravated money laundering can mean up to five years in prison.