The attack, a day after an attempted bomb attack to snatch away a death row militant, has been reported Tuesday on the Dhaka-Chittagong Highway at the Chandina Upazila.
Highway police's Sub Inspector Kamal Uddin said a 'Shyamoli Paribahan' bus was stopped by the police check-post on the highway at the Upazila's Teerchar Village around 11am.
"The law enforcers retaliated by opening fire and the two were nabbed while trying to flee," he told bdnews24.com.
Police have identified the two as 'Jashim', 30 and 'Hasan', 32, but could not provide any other details.
"The check-post was engaged in a routine search. The vehicle was stopped for speeding.
"When the police were going through the documents, the two came down and hurled bombs shouting 'Allahu Akbar.' No one was injured as the bombs did not explode," said Highway police's Deputy Inspector General (DIG) Atiqul Islam.
The other one threatened to explode a bomb in his hand, but was later caught.
"They belong to militant organizations. One of them has been sent to the Comilla Medical College Hospital with wounds sustained after police opened fire. The other one is being questioned," said DIG Islam.