Strikes and actions by trade unions have also been banned.
But the regulations state that rallies may be organised "for religious, social, state or government purposes".
The government has also banned "provocative" reporting.
"Under the gazette notification, the government can restrict publication or transmission of any anti-government news, editorial, post-editorial, article, feature, cartoon, talk show or discussion in print or electronic media and any mass media, including the internet," the ministry of the interior said.
Political parties and the media did not immediately react to the restrictions, but the Committee to Protect Journalists, a New York-based organisation, released a statement saying: "These rules give authorities sweeping powers of censorship that will deprive Bangladeshi citizens of independent information at this critical time of political upheaval."
The statement quoted Joel Simon, the group's executive director as saying: "We call on the interim government to rescind these repressive rules immediately."
The regulations will remain in force until the government lifts the state of emergency, which was declared by Iajuddin Ahmed, the Bangladeshi president, on January 11.
The state of emergency came in the wake of growing violence in Bangladesh that had killed at least 45 people and left hundreds injured.
The election, originally planned for January 22, was put off after a political alliance headed by Sheikh Hasina, leader of the Awami League, staged protests and called for reforms to the election process.
These included an overhaul of the voters' list to remove fake entries and the reconstitution of the election commission by dropping officials Hasina accused of a bias towards, Begum Khaleda Zia, leader of the Bangladesh Nationalist Party.