Their associate Sheikh Sunny Mostafa was also placed on a three-day remand
Dhaka Metropolitan Magistrate Rajesh Chowdhury placed them on a four-day remand on Tuesday afternoon.
The court also rejected their bail petitions and placed their associate Sheikh Sunny Mostafa on a three-day remand.
General Recording Officer (GRO) of CMM court Sub-Inspector Shafayetul Islam confirmed the news to Dhaka Tribune.
Earlier in the day, CID Inspector Mehedi Maksud, also the investigation officer of the case, produced the trio before court with a 10-day remand plea for each of them.
Enamul Haque Enu is the director of Dhaka Wanderers Club and vice-president of the Awami League's Gandaria unit, while his brother Rupom Bhuiyan is the joint general secretary for the same area.
At least four cases had been filed against the brothers for their alleged ties to illegal casino business, money laundering and corruption.
CID officials arrested Enamul, his brother Rupon and their associate Sunny from Dhaka's Keraniganj on Monday morning.
CID Deputy Inspector General (Organized Crime Unit) Imtiaz Ahmed said Enamul and Rupon were trying to escape the country with counterfeit passports.
He also said that the two Awami League leaders have 22 properties altogether in Dhaka and Tk19.11 crore in their 91 bank accounts. The bank accounts have now been blocked.
Meanwhile, the law enforcement agencies have still been investigating to determine more of their illegal wealth and assets.
On September 24, 2019, Rapid Action Battalion (RAB) seized about Tk5 crore in cash, eight kilograms of gold - worth over Tk4 crore and six firearms during raids on their residences.
The duo had been on the run following the crackdown.