Police initially arrested all 26 men after Singapore deported the group for supporting "armed jihad ideology", but later released 12 after finding no evidence against them.
"We have primarily found their connection with ABT," deputy police commissioner Mashruqure Rahman told AFP, referring to the banned Islamist group Ansarullah Bangla Team.
He said the detained men were followers of Jashim Uddin Rahmani, a firebrand cleric and ABT leader who was jailed last month for abetting the 2013 murder of secular blogger Ahmed Rajib Haider.
The government has so far made no comment on Singapore's announcement Wednesday that it had arrested 27 Bangladeshi construction workers who were being groomed to return to their home country to wage holy war.
The Singapore government said the men had "shared jihadi-related material discreetly among themselves, and held weekly meetings and gatherings where they discussed armed jihad", although they were not planning attacks in the city-state.
A 27th Bangladeshi is serving a jail sentence for attempting to flee Singapore after learning about the arrests of the other group members.
Tensions are high in Bangladesh after five more secular bloggers and a publisher were brutally killed last year.
There have also been attacks on minority Sufi and Shiites Muslims and several foreigners have been murdered in recent months.
Analysts say Islamist extremists pose a growing danger as a long-running political crisis in the majority Sunni Muslim but officially secular country has radicalised opponents of the government.
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