Chan Tan Chou, Al Jazeera's correspondent in Kathmandu, said: "People are very frustrated but they’re also very intimidated because these people are travelling in mobs swinging batons and creating a lot of noise.
"Protests like this, and of course there are smaller scale ones as well, have been going on every other day to keep up the pressure on the new government," he said.
Police have said they do not yet know how Phuyal died or who is responsible.
But the former Maoist rebels have blamed the youth members of another rival party for the death and demanded that those involved be arrested.
The former Maoist rebels ended their decade-long armed struggle against Nepal's government three years ago and entered a peace process.
They won general elections in 2008 and Pushpa Kamal Dahal, the top rebel leader, became prime minister which forced the abdication of the king.
Last month, Dahal tried to fire the head of the country's army, in part for not integrating the former guerrillas into the armed forces. When the president overruled his order, Dahal resigned as prime minister.
Since then they have been pushing to finalise the peace process by having their former fighters incorporated into the national army.
But the army, a bastion of Nepal's former ruling elite, accuses the Maoists of not fulfilling their commitments to return property grabbed during the civil war and disband its YCL.