The government is trying to settle several overlapping conflicts in the south so a national election can be held in November for a special assembly that will draft a new constitution and determine the country's future political system.
Upendra Yadav, the Madhesi group's leader, welcomed the pact, saying the Madhesi people "who had been oppressed for centuries will go to the November polls and shape our future ourselves".
Poudel said the government also agreed to recognise their language in offices and schools and to work on reserving government jobs for Madhesi people.
Many southerners say their region has been neglected in favour of the more populated, mountainous north.
They are demanding greater autonomy, more seats in the national legislature, and a guaranteed number of representatives in the administration.