Other government and election officials confirmed that the January 8 polls would be postponed.
Bhutto's party rejected any delay and insisted the government should stick to the schedule, but a spokesman for Nawaz Sharif, another major opposition leader, said a short postponement "would be acceptable."
The vote is under scrutiny around the world as President Pervez Musharraf pledges to complete the Islamic nation's transition to civilian-led democracy after eight years of his military rule.
Bhutto's murder during a campaign rally last Thursday however changed the atmosphere, unleashing a wave of deadly violence.
"Certainly it will be pushed back for at least four weeks if not more," the cabinet official said.
A government official told AFP separately: "It is out of the question that the elections will be held on January 8 because of the widespread unrest that has directly affected election staff and vote preparations."
He said logistics and preparations had been disrupted by unrest in Sindh province, the heartland of the Bhutto family and its supporters, while ballot printing in the country's biggest city Karachi was behind schedule.
"More than 40 offices of the election commission and its administrative offices have been damaged in Sindh," the government official said.
The election commission official agreed: "No doubt, the elections are going to be delayed."
Pakistan has faced international calls to stick to the planned date for the elections since Bhutto was killed in a gun and suicide bomb attack at a rally in the northern city of Rawalpindi.
Her party, which Sunday named her 19-year-old son Bilawal as its new leader alongside her widowed husband Asif Ali Zardari, insisted it wanted the polls held on their original date.
"We are ready for elections and do not want any delay. We demand immediate elections -- and on January 8," senior party official Shah Mahmood Qureshi told AFP.
"The government should stick to the schedule. If the government delays the election, we will call a central executive committee meeting to decide our future course of action," said Qureshi, a member of that committee.
A delay could spark disagreement over the caretaker government running the country. Officials in Bhutto's party say they do not trust it to investigate her death properly.
The unrest left at least 38 people dead as protesters torched hundreds of banks, shops, offices, trains and vehicles in a wave of violence that caused millions of dollars in damage, according to government estimates.
Election commission secretary Kanwar Dilshad told reporters earlier that it had asked provincial governments to report on the law and order situation by later Monday.
In addition, officials said, the announcement of the new date could not be made until after consultations with the major parties.
Tensions have eased and life in major cities is now almost back to normal, with shops and banks starting to reopen and cars, taxis and some buses on the streets. Schools remained closed.
Still, the Karachi Stock Exchange fell 4.7 percent in early trading Monday, which dealers said was one of the sharpest drops in memory.
The index, which had closed hours before Bhutto was killed, was down more than 680 points to 14,085.
The appointment of Bhutto's son, a student at Britain's Oxford University, extends the family's grip on the party leadership into a third generation.
But he is politically untested, and analysts believe real power will lie with Zardari -- a highly controversial figure mired in corruption allegations over kickbacks during Bhutto's premiership.
© 2007 Agence France Presse