The protests have clouded peace moves between the government and Maoists aimed at ending a decade-old conflict, which has killed more than 13,000.
The Madhesi People's Rights Forum rejected police claims that the demonstrators attacked police in Malangwa, saying the demonstrators were unarmed and the rally peaceful, until the police arrived.
Amresh Narayan Jha, a spokesman for the group, said: "These allegations are baseless. Our supporters have been hunted down by the security forces and killed even after the curfew was lifted."
In Birgunj, a commercial and business hub 60km southeast of Kathmandu, tens of thousands of protesters tried to march towards the main government building in the town, where one protester was killed and at least five wounded in police firing.
Shambhu Koirala, the chief administrator of Birgunj, said: "Police had to open fire in self-defence as protesters tried to storm the district administration office."
Witnesses said protesters shouting "Long Live Madhesi Unity" and "Fulfil the genuine demands of the Madhesi people" carried bamboo sticks and spears as they marched.
In Biratnagar, the home town of Girija Prasad Koirala, the prime minister, protesters beat up local journalists, Nepali television channels reported. Authorities said at least three towns were under curfew on Sunday.
The Madhesi group says ruling elites dominated by people from the northern hills have kept them out of jobs in the government, police and army, and seats in Nepal's interim parliament. They want an autonomous region for the southern plains within a federal state.
The government says it is ready for talks but protest leaders insist Krishna Prasad Sitaula, the home minister, whom they accuse of using excessive force, must resign before any negotiations take place.
The UN human rights office in Nepal has asked Nepalese security forces to stop using unnecessary force in the clashes with protesters.