Anger remained high on Friday in the city after the incident at around midnight on Wednesday when the soldier fired on a crowd of villagers who had gathered at a temple to mark the full moon.
The soldier, who had an argument with the villagers, also died in the incident in the tourist town of Nagarkot, near Kathmandu, but the circumstances of his death were not clear.
Ram Chandra Poudel, general-secretary of the Nepali Congress party, said: "King Gyanendra must take the moral responsibility for the killing." The king is also the country's defence minister.
The Nepali Congress is a constituent of an alliance of seven parties campaigning for the restoration of democracy after King Gyanendra fired the multi-party government in February and seized full control of the impoverished nation.
The Nepalese army, which said it had taken the incident very seriously, has ordered an investigation into the incident.
State television said the government would pay for hospital treatment and $2000 in compensation for each of the dead.
Nepal's King Gyanendra seized
full control in February this year
Friday's strike was called by the alliance to grieve for the victims of the shooting.
On Thursday, near the site of the killings, 2000 people, including relatives and friends of the victims, burned tyres and protested.
"You can't just kill people," they shouted outside a hospital where the bodies of the victims were taken for post-mortem examinations.
Dozens of riot police stood guard as relatives waited to receive the bodies.
Sohan Shrestha, who had come to collect the body of his son, said at the hospital: "I heard the sound of bullets as I was preparing to sleep. I was terribly scared."
Witnesses said the villagers had gathered to mark the full moon on Wednesday at the temple on a hilly terrace.
"I heard the sound of bullets as I was preparing to sleep. I was terribly scared"
Sohan Shrestha, a victim's father
Deepak Rijal, a journalist who visited the site, said: "Bloodstains littered the entire temple. The villagers are terrified."
Human-rights groups say the poorly trained Nepali army regularly commits human rights abuses in its battle to quell a Maoist rebellion.
More than 12,500 people have died in the anti-monarchy conflict, which has also shattered Nepal's aid- and tourist-dependent economy.