Those killed were members of the outlawed group Jamaatul Mujahedeen Bangladesh (JMB), said Home Minister Asaduzzaman Khan. Authorities have blamed the group for a recent spate of attacks in Dhaka and elsewhere in the country.
Different units of the Bangladesh police force raided three houses, two in the Gazipur district close to Dhaka and one in the Tangail district, about 60 miles from the capital.
Nine suspected militants were killed in Gazipur and two in Tangail, said Khan. All were killed in gunfights with police after refusing to surrender, he added.
Police recovered firearms and ammunition from the scenes, Khan said.
Authorities did not disclose the identities of the suspects killed, but Khan said one in Gazipur was a commander of JMB's Dhaka unit.
Prime Minister Sheikh Hasina said Saturday that her administration is determined to put an end to militancy and terrorism.
"We'll not allow any act of terror in the name of religion," she said while visiting Dhaka's minority Hindu community on Saturday.
In recent years, a number of Bengalis belonging to religious minority groups -- including Hindus, Buddhists, Christians and Shia Muslims -- have been killed in attacks by JMB and Ansar al-Islam, another militant group.
JMB is a Sunni Muslim extremist group that has pledged its allegiance to ISIS. It aims to transform Bangladesh into an Islamic state based on sharia law.
Minister Khan also said at a press conference on Saturday that police are closing in on one of the masterminds of the recent attacks, sacked army Maj. Syed Mohammad Ziaul Hoque.
"Major Zia is now under close watch and he may be arrested anytime," Khan said, using a nickname for the major used by intelligence officials.
Hoque went into hiding in 2011 after the military accused him of participating in a failed coup. He is believed to be working with Ansar al-Islam.