The stoppage was called by the opposition Awami League in response to a grenade attack on a political rally Saturday in Sylhet that killed 18 people. Shots were also fired in the attack, although opposition leader Sheikh Hasina escaped uninjured.
Most demonstrations were peaceful but police were out in riot gear, the BBC reported.
"We don't want to see any more death. This repressive government must step down right now," opposition leader Hasina told reporters, referring to Prime Minister Khaleda Zia.
Transport operators said there were few vehicles on the highways although a few trains and river ferry services were running. Cargo handling was completely stopped at the country's main port in the southern city of Chittagong, officials said.