The deceased were identified as Sujan Saha, a garment worker and son of Shankar Saha of Tanbazar; and Kalidas Saha, a pharmacist of Chashara.
Asit Baran Biswas, councillor of ward-15 of Narayanganj City Corporation, said Sujan had been suffering from fever and breathing complications for the last four days.
When he was taken to the Narayanganj 100-bed General Hospital on Saturday night, doctors suggested he received treatment staying at home.
However, he died around 3am on Sunday.
Meanwhile, Kalipad Saha, owner of Sabitri Pharmacy in Chashara, died on Sunday morning after he was sent to Dhaka Medical College Hospital.
He had been suffering from fever, sore throat and lung complications, councillor Asit said, adding that samples of the deceased were collected to ascertain whether they were infected with the coronavirus.