Rastriya Prajatantra Party-Nepal supporters clashed with police in front of the Constituent Assembly building, said Rajaram Shrestha, central committee member of the party.
The protest was led by the party's chairman Kamal Thapa.
The police baton-charged the agitators trying to enter the restricted area during which at least six activists were injured, according to police.
Some 2,500 RPP-Nepal supporters staged protest, demanding timely promulgation of a constitution and a provision to reinstate Nepal as a Hindu state in the new statute.
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The possibility of delivering a constitution by the deadline appears bleak as there persist several contentious issues for the political parties to sort out.
RPP Nepal in a statement threatened to launch an agitation if the parties failed to adhere to the deadline.
They said through the agitation they would demand referendum on key issues including secularism, fate of monarchy and federal structure.
In June 2008, Nepal's last king Gyanendra Shah stepped down after parliament voted to abolish the monarchy, and Maoist rebels ended their insurgency and joined politics.