The Maoists, led by the former prime minister Prachanda, have said that the president had undermined the supremacy of the civilian government in stopping them from acting.
"Unless the president's move is corrected, we will continue our protests"
former Maoist prime minister
"Our achievements have been hijacked and civilian supremacy has been hijacked. The main aim of our protest is to restore it," Prachanda said as he led the protest.
"Unless the president's move is corrected, we will continue our protests."
Thursday's demonstration is part of a fortnight-long series of nationwide protests being held by the former guerrillas, who fought a 10-year civil war against the state that ended in 2006.
The protest had started in celebratory mood, with activists dancing and playing traditional music as they handed round dishes of rice and curry.
But the atmosphere turned angry as the clashes broke out and one television station showed police using axes to destroy musical instruments left behind when the demonstrators fled.
Barshanan Pun, a Maoist MP, said that 20 protesters had been injured in the clashes.
Al Jazeera's Subina Shrestha, reporting from Kathmandu, said that the government was likely to give into some of the protesters' demands if the demonstrations continued.
"The government cannot work. Today no one, except the foreign minister, could enter the government houses - so this cannot continue for a very long time," she said.
"Both side have to compromise at some point because the Maoists do not want to go back to war. The government has not actuallly attacked the Maoists, it has still not gone all out against the Maoists.
The Maoists emerged as the largest political party in elections last year after agreeing a peace deal in 2006 and got the 239-year-old monarchy abolished through a special assembly which turned Nepal into a republic.
But they quit the government after the dispute with the president.