Police can request an extension if they need more time to interrogate them.
Mohammed Jalaluddin, who is in charge of investigating the case, said there was no lawyer present today to seek bail for the suspects.
A spokesman for the elite anti-crime force Rapid Action Battalion, Maksudul Alam, said the suspects include the alleged head of the group in Bangladesh. He said they were arrested in raids starting Wednesday.
Cmdr Mufti Mahmud Khan, another spokesman for the anti-crime agency, told reporters that officers "seized explosives, bomb-making materials, knives and books on jihad" from some of the suspects.
In May, al-Qaida's Indian subcontinent branch claimed responsibility for the murders of two secular bloggers, including a Bangladeshi-American, who were critical of Islamic fundamentalism.
Al-Qaida launched the South Asian branch last September, saying it would take its fight to Myanmar, Bangladesh and India.