Nepal's parliament voted on Saturday to amend the country's new constitution in a bid to resolve a months-long dispute with ethnic minority protesters demanding more political representation.

"I announce that the Nepal constitution first amendment bill has been passed with a two-thirds majority in favour," said speaker Onsari Gharti Magar as lawmakers thumped their desks in agreement.

More than 50 people have been killed in clashes between police and people protesting against the constitution introduced in September, which demonstrators said left them politically marginalised. 

Demonstrators from the Madhesi ethnic minority, mainly from Nepal's 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 an effort to end the deadlock, parties last month tabled a bill to amend the constitution and increase the Madhesi presence in government bodies through proportional representation.

But Madhesis say the bill is incomplete and does not address their main demand to revise the federal state borders laid out in the charter that will limit their representation in parliament.

Madhesi lawmakers walked out of parliament in protest before the bill was passed late Saturday with 461 votes in favour of the amendments. 

Seven voted against it, and the remaining 128 MPs were either not present or part of the walkout.

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 had failed to reach an agreement.