The shootings took place as thousands of protesters around Kathmandu tried to break through police cordons, set up to prevent them from reaching the center of the capital.
They marched Thursday in defiance of a day-long curfew and shoot-on-sight orders issued to Nepalese police.
This protester says he wants the king to give democracy back to the people. He says many people do not have enough food to eat, but they are still out demonstrating against the king.
Last year, King Gyanendra dismissed parliament, and restricted civil liberties, because, he said, political parties failed to bring stability to the country, which is coping with a 10-year communist insurgency. He promises parliamentary elections next year.
The protests Thursday are the largest in 15 days of anti-government rallies. At least eight other people were killed in earlier demonstrations.
A coalition of seven mainstream political parties is behind the protests, which the parties hope will pressure King Gyanendra to restore democratic freedoms - that is what the parties demand, before they will talk with the government.
Since the king seized power in February 2005, police have arrested hundreds of opposition politicians, activists and students. Many remain in detention after the latest wave of arrests earlier this month.
A senior envoy, Karan Singh, delivered a letter to King Gyanendra Thursday on behalf of the Indian prime minister. No details were given about the letter's contents, but Singh has said India wants to assist all parties in Nepal find a way out of the political crisis.
Rhoderic Chalmers, an analyst with the International Crisis Group, says India is one of many countries trying to pressure King Gyanendra to compromise, so that talks with opposition parties can take place.
"I'm sure that will be the message from the Indian side - that the game is up, this is now your final chance to make a compromise. But, if you do that, we are here, ready to help, and we want a smooth transition to a stable settlement. That is India's fundamental interest. It is the outside world's fundamental interest," said Chalmers.
The United States and the United Nations also have called on the king to open up talks with the opposition.
The political stalemate in the capital is not Nepal's only problem.
Communist insurgents, calling themselves Maoists, are in control of much of the countryside, in a conflict that has claimed more than 11,000 lives. The rebels have formed an informal alliance with the opposition parties, as part of their efforts to topple the monarchy.
]]]Witnesses say the troops opened fire on a large crowd of protesters Thursday in Kalanki, on Kathmandu's western edge. They also used tear gas.
Hospital officials in Kathmandu say they are treating injured people.
The VOA correspondent in Nepal says several thousand protesters on the edge of the capital are marching toward a line of police, trying to push into the center of the city.
Nepal's opposition parties had said their protest march into Kathmandu would go ahead despite the curfew ordered by King Gyanendra's government. An 18-hour ban on all movements in and around Kathmandu is in effect until 2000 local time
Today's deaths bring to 12 the number of people killed during two weeks of protest rallies in Nepal, called to denounce the king's seizure of absolute control last year.
Five people died during Wednesday's protests.
King Gyanendra dismissed Nepal's elected government 14 months ago, saying the officials then in power had been unable to control a Maoist rebel insurgency in the Himalayan nation.