Fears of violence increased after the Young Communist League, a Maoist youth wing, held exercise sessions in public and school fields in the capital.
"We have been training our cadres with physical exercises in order for them to be better able to control the crowd if the protests turn nasty," Pushpa Kamal Dahal, a Maoist leader and former prime minister, commonly known as Prachanda, told reporters earlier in the week.
"But our protest will be peaceful. We will not use violence."
The former rebel group had led a coalition government after winning polls in 2008, but resigned from government after Prachanda was prevented from firing the army chief.
"The protests are to press for a new government based on the national consensus," Narayan Kaji Shrestha, a senior Maoist leader, told the Reuters news agency.
"Since our party is the biggest in the constituent assembly we must be allowed to lead the new government."
The Maoists still hold the largest number of seats in parliament.
Dahal has said that if the government does not meet their demands a nationwide indefinite strike will be held from May 2.
The current government has accused the Maoists of not being committed to democracy and says they have not disbanded a paramilitary group linked to them.
Nepalese legislators have until May 28 to produce a new constitution aimed at securing peace after the end of the civil war and the removal of the royal family in 2006.