The tribunal in Dhaka was set up by the Bangladeshi government.
For the first time, charges were due to have been brought against those accused of committing mass murder and rape.
Most of those facing trial are from the Islamist party, Jamaat-e-Islami. All of them deny the allegations, accusing the government of carrying out a vendetta.
The tribunal in Dhaka will reconvene on 18 August following a request by defence lawyers, who wanted more time to go through the charges.
East Pakistan became Bangladesh 40 years ago - but only after a bloody battle for independence.
Official figures estimate that more than three million people were killed and thousands of women raped when West Pakistan sent in its army to intervene.
Last year, the Bangladeshi government set up the International Crimes Tribunal in Dhaka to try those Bangladeshis accused of collaborating with Pakistani forces and committing atrocities.
So far, seven people - two from the main opposition Bangladesh Nationalist Party and five from the Jamaat-e-Islami - have been arrested. Formal charges are yet to be brought against them and all of them deny the charges.
The two parties have denounced the tribunal as a political show trial.
The New York-based Human Rights Watch says the tribunal needs to change some of its procedures to ensure a fair trial which meets international standards.
The trial - when it finally starts - is likely to go on for months and open up old wounds.
A special tribunal in Bangladesh to look into atrocities carried out during the war of independence from Pakistan in 1971 has been adjourned.