The deaths came amid mass protests by the BNP on the first anniversary of the controversial 2014 parliamentary elections in Bangladesh. BNP opposition leader Khaleda Zia has urged supporters to participate in anti-government rallies on Monday.
"Two people have died from injuries suffered in violent clashes. We've come to know that they are involved in BNP politics," Moshiur Rahman, the district's administration chief, was quoted as saying by Xinhua Monday.
In addition, dozens of people were injured during the protests, the agency said, citing local police sources.
Last week, Zia urged its supporters to take to the streets on Monday, demanding new multi-party elections, the local media reported.
The head of BNP has been held captive in her office in Dhaka, the capital of Bangladesh, since Saturday night.
On January 5, 2014, the Prime Minister of Bangladesh, Sheikh Hasina, who had been in power since 2009, was reelected for additional five-year term. However, the main opposition parties, including the BNP, boycotted the voting claiming the parliamentary elections were fraudulent.