The military marked the public holiday with a dawn artillery barrage and people poured into the streets chanting ''victory is forever, let us keep it safe''.
Bangladesh won independence from Pakistan on December 16, 1971, after a nine-month guerrilla war in which millions died.
Addressing a parade in Dhaka, President Iajuddin Ahmed urged Bangladeshis to make the impoverished country a happy and prosperous nation.
The president lay a wreath at the national war memorial at Savar, 25 km from the capital, followed by rival former prime ministers Begum Khaleda Zia and Sheikh Hasina, witnesses said. Security was tight.
Khaleda's Bangladesh Nationalist Party (BNP) and Hasina's Awami League are vying for power in elections on January 23.
The run-up to the polls has been violent and tense with rival activists clashing almost daily. At least 44 have been killed and hundreds injured since late October.
Twenty people were wounded in clashes among rival student groups in Mymensingh Agricultural University 130 km north of the capital Dhaka during celebrations.
Part of a dormitory was sent on fire and several rooms at another were vandalised. Police used batons to disperse rival groups fighting with sticks and stones.
At least 10 people were injured in fighting overnight when rival party officials gathered to lay wreaths at a war memorial in the southern port city of Chittagong, police said.
Bangladesh was focused on holding a free and fair election, with a Hasina-led multiparty alliance threatening to ''resist'' unless crucial reforms are implemented.
Its demands include removal of key Election Commission officials, whom Hasina accuses of bias in favour of Khaleda and the BNP, and pushing back the poll date to allow more time for campaigning.
Officials said this was a remote possibility because the constitution requires elections within three months of the expiry of the previous government's tenure.
Khaleda handed power to Iajuddin on October 29 at the end of her five-year term as prime minister. He now heads an interim government charged with organising the elections.
Hasina has accused Iajuddin too of bias towards Khaleda and urged him to quit as caretaker leader to prove his neutrality.
The BNP attacked Hasina, saying she was trying to destroy democracy and push Bangladesh into a constitutional crisis.