The tragedy happened in the Jamal Khan area at a memorial event organised for the minority Hindu community, The Daily Star reported from the port city.
A police official said all of the dead were men who had been attempting to attend the event.
The death toll is expected to rise as several others have been seriously injured in the incident at a convention centre, officials said.
"According to information we received, 10 people were killed," a home ministry spokesman told PTI.
The incident happened at the entrance of the two-storey building.
With the crowd swelling out of control, people jostled for space on the ramp outside the entrance forcing some visitors to fall only to be trampled on by those behind, Bdnews24 reported.
Reports from Chittagong suggest nine of the dead were Hindus with the 10th being a Buddhist.
Mohiuddins family announced Taka 100,000 in compensation for each of the families of the dead, said Awami League's Chittagong City unit Deputy Office Secretary Jawaharlal Hajari.
They will also receive an additional Taka 5,000 for the funeral and the family will also bear the cost of treatment for those injured, said Hajari, who was in charge of the event at the community centre.
Thousands of people joined the "Qul-khwani" staged simultaneously at 14 convention centres where lunch was served as part of the rite.
Stampedes during religious events are not rare in Bangladesh. In 2015, two incidents left 37 people killed.
As many as 10 people, seven of them women, were killed during a Hindu ritual bath in Narayanganj in March 2015.
In July, 27 people all of them women and childrendied in Mymensingh where thousands of people had gathered for a free Zakat clothes giveaway.
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