Earlier, Khawaja Asif, a senior leader PML-N leader, said: "It will be in his own interest, it will be in the interest of his party and it will be good for the system."
Siddiqul Farooq, a spokesman for the party, also called for Zardari to step down, saying the president should "resign on moral grounds" and "not depend upon the crutches of the constitution".
Pakistan's constitution guarantees Zardari immunity while in office.
But the constitution also states that presidential candidates must be pious, honest and truthful and not have been convicted in a criminal case.
Pakistan's anti-corruption body has called for travel bans to be imposed on more than 250 people since the supreme court ruling.
Ahmed Mukhtar, the country's defence minister, told local television late on Thursday that he had been due to go on an official visit to China but that his name had been put on an "exit control list" restricting travel.
"I was informed that my name is on the exit list ... federal investigation authorities officials have said that I cannot leave the country," he said.
"It was in connection with a corruption case. But there is no corruption case against me - it is only an inquiry which is pending against me for the past 12 years. I will strongly defend myself in the court."
The supreme court's decision on Wednesday declaring the amnesty agreement as being unconstitutional paves the way for corruption cases against Zardari and thousands of other officials covered by the amnesty to be revived.
"All the cabinet members must immediately tender their resignations," Farooq said.
Beneficiaries of the amnesty include Pakistan's interior and defence ministers.
A number of cases were pending against Zardari when it was announced by Pervez Musharraf, then Pakistan's president, that he and others would be immune from prosecution under the 2007 National Reconciliation Ordinance (NRO).
Musharraf declared the NRO while under pressure to hold elections and end eight years of military rule.
Although Zardari has spent years in jail over corruption charges, he alleges the charges were politically-motivated and questions hang over whether he was ever actually convicted.
Zardari's Pakistan People's Party (PPP) won elections in 2008, restoring civilian rule, but the NRO expired at the end of last month and the PPP did not have enough support to renew the ordinance in parliament.
Senior figures in the PML-N, led by Nawaz Sharif, a former prime minister, have already called on Zardari to give up powers inherited from Musharraf such as those to sack the prime minister and dissolve parliament.
Zardari already faces low public approval ratings and any political trouble in Pakistan is likely to be watched very closely by the West which wants Islamabad to focus on combating Islamist fighters.