"The CBSA (Canada Border Services Agency) has decided not to pursue detention for these individuals," CBSA spokeswoman Faith St. John told AFP.
Instead, "the CBSA is proceeding with each case in accordance with the specific facts and the appropriate process under the Immigration and Refugee Protection Act," she added.
Paula Faber of the Immigration and Refugee Board said it has so far ordered 50 of the 76 to be released with "terms and conditions" and 18 of these have been freed.
Now, all of them could be released within weeks, officials said.
The Canada Border Services Agency had singled out 25 of the group as possible Tamil Tigers -- a separatist group that waged a decades-long civil war with the government of Sri Lanka.
The Liberation Tigers of Tamil Eelam (LTTE) are banned in Canada as a terrorist group.Last month, the Canadian government told the immigration panel that the "Ocean Lady" freighter used to transport the migrants was linked to the LTTE and had possibly been used for arms shipments.
Tests showed two of the men detained had explosive residue on their clothes, officials said.
The LTTE, popularly called the Tamil Tigers, fought a brutal separatist war against the Sri Lanka government from 1976 until it was defeated last May.
Thousands of Tamils remain in refugee camps in the country while ships carrying Tamil migrants fleeing Sri Lanka have also been reported off the coasts of Australia, Malaysia and Indonesia.