Clashes broke out in the southeastern district of Morang on Thursday afternoon when hundreds of protesters armed with batons, knives and petrol bombs tried to disrupt a meeting of activists from the ruling CPN-UML party.
"Three were killed in Morang in two clashes today," police spokesman Kamal Singh Bam said, adding that the victims included a 65-year-old woman, one of two killed at the activists' programme venue.
A 25-year-old man also died when police opened fire on protesters as they attempted to stop a public bus.
Nepal police gunfire kills Indian national at border protest
"The police were forced to fire after the protests became violent," Mr Bam told AFP.
Demonstrators from the Madhesi ethnic minority, mainly from the southern plains, have led a months-long blockade of a key border crossing, causing a crippling shortage of fuel and other vital supplies across the landlocked country.
In a bid to break the deadlock, parties tabled a bill to amend the constitution and increase the Madhesi presence in government bodies through proportional representation.
But protesters say the bill, currently under discussion in parliament, is incomplete and does not address their main demand to revise the federal state borders laid out in the charter.
Nepalese police shooting kills four including child
The Constitution, the first drawn up by elected representatives, was meant to cement peace and bolster Nepal's transformation to a democratic republic after decades of political instability and a 10-year Maoist insurgency.
But several rounds of talks between the government and the protesting parties have failed to reach an agreement.
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