The commission will consult political parties before announcing a new date for the elections, local TV channels said, referring to electoral officials.
On December 27, the country was plunged into turmoil following the killing of Bhutto, who had twice been the country's prime minister and was about to run in parliamentary elections January 8 as leader of the Pakistan People's Party (PPP).
Thousands of Bhutto supporters took to the streets chanting anti-government slogans as protests spread across the country. Shops, offices, buses and even police stations have been attacked and set on fire leaving at least 30 people dead.
Thousands of extra police and troops have been deployed to try and deal with the violence.
Russia has condemned the terrorist attack and urged Pakistan's political forces to exercise utmost restraint and not to respond to any provocation.
