Police fired at demonstrators from the Madhesi ethnic minority after they vandalised a police post and a revenue office and set on fire government vehicles, defying curfew clamped in Parsa district's Birgunj municipality which borders Raxaul town in Bihar.
Four protestors were killed and several others were injured in the clash, Home Ministry spokesperson Laxmi Prasad Dhakal said.
In another incident, a 22-year-old protester died during a clash with police in Kalaiya town of Bara district.
The Joint Madhesi Front has enforced an indefinite strike in Parsa and neighbouring districts in southern Nepal to protest the draft constitution and seven-province federal model proposed by the major parties on August 15.
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The Madhesi parties are demanding autonomous region in the Terai, the southern plains and more rights and representation for the Madhesi people living in the southern Nepal.
The ethnic groups say having a separate state would give them a stronger say in local affairs.
The main political parties now agree that there should be seven federal states, but smaller political parties and ethnic groups oppose either the number or the structure of the states.