A commander of the elite Rapid Action Battalion (RAB) force said they died in an "apparent suicide bomb blast" on Monday.
The blast occurred on the outskirts of Comilla town, 150km south of the capital, Dhaka.
Two RAB members were also inured, police said.
They said two rebels were arrested at the badly damaged house, including the son of Shayek Abdur Rahman, a leading rebel captured previously.
Abdur Rahman led the outlawed Islamist group Jamaat-ul-Mujahideen, which police have blamed for a wave of bombings.
Police said Monday's operation was directed at capturing Mohammad Salahuddin, a close associate of Abdur Rahman, who surrendered on 2 March in the northeastern town of Sylhet.
A local police officer said: "We didn't get Salahuddin but had a surprise catch, Nabil [Abdur Rahman's son]."
Another leading rebel, Siddikul Islam Bangla Bhai, was captured in a gun battle in northern Mymensingh district on 6 March.
Abdur Rahman has been held for interrogation while Bangla Bhai is being treated at an armed forces hospital in Dhaka for injuries he suffered during his capture.
The outlawed Jamaat-ul-Mujahideen and Bangla Bhai's group, Jagrata Muslim Janata Bangladesh, are fighting for the introduction of sharia law in Bangladesh, a mainly Muslim democracy.
They have killed at least 30 people and wounded 150 in countrywide bomb attacks since 17 August last year, but the government says the Islamist network has been shattered after the capture of the two key leaders.