The minority Madhesi in the southern plains say that the new charter consolidates the power of the country's hill elite and marginalises them in the way new states will be created in a federal structure.
Nepal has been struggling to establish a stable republic following the abolishment of a 239-year-old Hindu monarchy in 2008 and is set to hold local polls in May that will be followed by national elections under the charter adopted in 2015.
But seven Madhesi parties issued a statement late on Wednesday saying they were cutting off support for Prime Minister Prachanda's government for failing to amend the constitution to reflect their grievances and vowed to disrupt the elections.
Govinda Acharya, an aide to Prachanda, said the former Maoist rebel commander was ready to meet Madhesi leaders to bring them on board but would not cancel the polls.
"There is no chance of calling off the polls. The prime minister is firm on this," Mr Acharya said. The government remains in majority in parliament despite loss of support.
Hridayesh Tripathi, of the Tarai Madhes Loktantrik Party (TMLP), campaigning against the constitution, warned of trouble in the plains where more than half of Nepal's 28.6 million people live if the polls went ahead without amending the constitution.
Five people were killed last week when police opened fire to break up protests against the constitution in the Tarai.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)
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