However, Pakistan's supreme court removed this amnesty in December last year and ordered the NAB to reinvestigate all corruption cases.
"In light of directions of the court on the revival of the Swiss cases, the NAB has initiated the process," Abid Zuberi, the NAB lawyer, told the court.
Judicial authorities in Switzerland said in August 2008 they had closed the money-laundering case against Zardari and released $60 million frozen in Swiss accounts for a decade after Pakistan dropped out of all cases it had initiated there.
Zardari has denied any wrongdoing and has said that in any case he has immunity from prosecution as president.
However, the events threaten to raise tensions between the judiciary and government, which could lead to an end to that immunity.
Zardari has had tense relations with Iftikhar Chaudhry, the current independent-minded supreme court chief, who was sacked in 2007 by Pervez Musharraf, the then Pakistani president.
Zardari promised to reinstate Chaudhry after his party formed a government in 2008 but dragged his feet and only did so in March 2009 when protesting lawyers and opposition supporters were converging on Islamabad for a protest rally.
And as a reminder of the violence that brought Zardari to power, a UN panel's report on Benazir Bhutto's assassination was due to be presented on Tuesday but was delayed until April 15 at Zardari's request.
"We requested them to include the views of three countries which had warned [Bhutto] after her return that she should take extra precaution because they had information she would be assassinated," Farhatullah Babar, a presidential spokesman, said.
Tariq Perzada, a political analyst and a columnist told Al Jazeera from Islamabad that Zardari's request for the report to be delayed creates many doubt.
"It comes as a shock and a surprise that Mr Zardari, the president of Pakistan and the husband of Benazir Bhutto, happens to be himself the person who has asked the United Nations to delay this report.
"If the report is delayed that will create credibility problems for the UN and creates a major credibility problem for the husband of the late Benazir Bhutto who is also partially suspected in this country."
The developments come against a backdrop of violence linked to the US-backed military campaign being waged by Zardari's government against the Taliban and al-Qaeda in the country's northwest.
In the latest incident, the Pakistani military said that six of its soldiers and 20 Taliban fighters were killed in a battle in the North West Frontier Province on Wednesday.
About 80 to 100 Taliban armed with rockets, guns and suicide vehicles attacked a paramilitary Frontier Camp at about 2am (2100 GMT) near the town of Bara in the Khyber tribal district.
"Security forces effectively responded and repulsed the attack. During an exchange of fire with security forces, about 20 terrorists were killed and more than 30 were injured," the army said.
Intelligence officials said that, in a separate incident, at least six alleged Taliban fighters were killed in North Waziristan in a suspected US drone attack.
Analysts say the Zardari's mounting judicial problems could hamper his government's ability to focus on economic issues and the war with the Taliban.