Candidates backed by the BNP have been elected chairman in the Upazila council elections at Bandar in Narayanganj and at Naldanga in Natore.
In Chuadanga, BNP's Sadar Upazila unit president Shamim Reza Dalim announced the strike on Monday.
The strike will be observed from 6am to 2pm on Tuesday in protest against rigging and forcible takeover of polling stations on Monday , he said.
In Sirajganj, Pro-BNP chairman candidate Iqbal Hossain Hiru of Shahjadpur Upazila alleged his polling agents were driven out from centres within hours after the polls began.
He said he informed the local administration but they did not respond appropriately.
"We will observe a half-day strike in the Upazila on Tuesday to protest these incidents, but we are not boycotting polls," Hossain said.
But in many places, BNP-backed candidates have withdrawn from the contest.