Security forces have launched a major crackdown on suspected Islamist militants since jihadists raided a Dhaka cafe in July and left 22 mainly foreign hostages dead.
But the crackdown which has seen a string of suspects killed in gunbattles has sparked concerns that opposition activists were among those being targeted.
Senior police officer Azbahar Ali Sheikh said a Jamaat-e- Islami party leader from the western district of Jhenaidah and a leader of its student wing were killed early today.
Top human rights activist Nur Khan Liton demanded a judicial probe into the killings.
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"We've serious questions about these deaths. We think these are extrajudicial killings," he told AFP, saying local newspapers had earlier reported the Islamists missing.
A senior Jamaat official denied the two party figures were killed in gunfights, saying both had been picked up by plain-clothed policemen early last month.
"It is cooked up (by police)," he told AFP on condition of anonymity.
The government has launched a nationwide crackdown on Jamaat activists in recent years, following deadly protests in which tens of thousands of Islamists were either detained or charged.
Bangladesh has also been reeling from a wave of recent attacks by Islamists, with targets including foreigners, rights activists and members of religious minorities.