A magistrate court in Dhaka rejected the detainees' bail plea on Sunday.
Defence lawyers argued that it was still unclear whether the seized two-pound material was indeed uranium, a heavy and dense radioactive element.
One of the lawyers claimed the detainees did not have the ability to store uranium.
It is still unclear how the men got hold of the suspected radioactive material.
Uranium is primarily used as fuel in nuclear power plants and to produce isotopes for medical and industrial purposes.
Enriched uranium is used to power nuclear ships and submarines, and nuclear weapons.
Depleted uranium, leftover after enriching ordinary uranium, is used in shells and projectiles to enhance their armour-piercing capacity.
There are no known sources of uranium in Bangladesh but its bordering Indian state of Meghalaya is believed to have a huge deposit of high quality uranium.
Police claimed the detainees identified the material as uranium.