The move is expected to end months of political tensions, but it was not immediately clear when the national assembly would vote on it.
"The Friday meeting has been adjourned and no date has been confirmed," Kamal Hyder, Al Jazeera's correspondent in the Pakistani capital, Islamabad, said.
Both the upper and lower houses of parliament can debate the issue for up to three days.
Known as the 18th Amendment Bill, the legislation seeks to reverse constitutional changes adopted by Pervez Musharraf, the former military ruler, effectively turning Zardari into a titular head of state.
"This [reform] package ... ensures provincial autonomy, judicial autonomy and effectively strengthens parliamentary democracy in the country"
associate professor at Quaid-e-Azam University
Drafted by a parliamentary committee made up of all political groups, the bill is expected to be passed by more than the two-thirds majority needed.
Ishtiaq Ahmed, an associate professor of international relations at Islamabad's Quaid-e-Azam University, said the move to undo reforms put in place under a military regime was important for Pakistan's institutional development.
"This package ... goes beyond stripping the president of Pakistan of arbitrary powers, it ensures provincial autonomy, judicial autonomy and effectively strengthens parliamentary democracy in the country," he told Al Jazeera.
Asked if the move would transfer too many powers to the prime minister, Ahmed said: "In a parliamentary system the chief executive has to be the prime minister, not the president."
Under the bill, the president would lose the power to dismiss the prime minister. It would also allow prime ministers to be eligible to stand for three terms in office.
That would allow Nawaz Sharif, the opposition party leader, who has already served two terms before being toppled in Musharraf's 1999 coup, to again become prime minister.
The president would also no longer be able to dissolve elected parliaments or appoint the commander of Pakistan's armed forces, as has been done in the past.
Zardari would also lose the power to appoint judges to a commission consisting of senior judges and government figures.
The bill has been heralded as a move that could ease instability in Pakistan, but it could also pave the way for corruption cases to be brought against the president.
The government is facing mounting pressure from the supreme court to reopen corruption cases against Zardari after it threw out a controversial amnesty law in December.
Zardari has summoned a joint session of parliament on Monday and will be addressing the combined session, Farhatullah Babar, the presidential spokesman, said.
In another development on Friday, Anwar Mansoor, Pakistan's attorney-general, resigned over what he said was the government's obstruction of supreme court orders to investigate the president for corruption.
Mansoor said the law ministry had been denying him access to documents needed to carry out the supreme court order.
"The supreme court is our top institution, and there is no way you can defy its orders," he said after announcing his resignation.
The supreme court has zeroed in on one case that had been taken up by the Swiss government against Zardari that was halted in 2008 under the amnesty.
Zardari and his late wife Benazir Bhutto, the assassinated former prime minister, were found guilty in absentia in a Geneva court in 2003 of laundering millions of Swiss francs.
They were handed six-month sentences and fined, but both punishments were automatically suspended when they appealed.