Groups of protesters took to the streets of the capital Kathmandu hours after the king's midnight message, chanting "Gyanendra, thief, quit the country" and "Down with autocracy, end police repression".
Riot police arrested about 20 demonstrators, but there was no violence on Friday.
Scattered protests continued through the day, but were not as intense as in previous days because it was a holiday for the Nepali Hindu New Year.
Political parties leading the movement against the king were quick to reject his offer for elections, saying the monarch's new year message would not defuse the fierce campaign in which four people have been killed and hundreds wounded in the past week.
Girija Prasad Koirala, president of Nepal's largest political party, said: "If the king doesn't listen to the voice of the people, I can only say, 'god save the king'".
Nepalis had hoped the king's traditional new year message would contain some new steps to ease tensions but it was largely a repeat of earlier promises to hold elections by April 2007.
King Gyanendra's new year
message failed to impress
He sacked the government and assumed total power in February 2005.
"It is our wish that in order to re-energise multi-party democracy there should not be any delay in reactivating all representative bodies through elections," the king said.
"May the efforts at ensuring sustainable peace and meaningful democracy in the interests of the nation and the people bear fruit during the new year."
Too little, too late
Senior leaders of an alliance of Nepal's seven main political parties, who are demanding the restoration of a representative government immediately, said his offer was too little, too late.
"He did not address the problem of the nation, he should have done that," said Koirala, 84, a four-time prime minister.
"He is not willing to reconcile with the opposition. The battle will go on. There will be chaos, violence, riots, for a few months or a few years"
Sher Bahadur Deuba
former prime minister
"There is no change (in his stance), all he has changed are only his words. We will start our agitation as usual and it will go on till the sovereignty of the people is not returned."
Sher Bahadur Deuba, who the king sacked as the prime minister 14 months ago, said the monarch had offered nothing new.
"He is not willing to reconcile with the opposition," he said.
"The battle will go on. There will be chaos, violence, riots, for a few months or a few years."
Maoist rebels, who are fighting to overthrow the monarchy and have joined hands with mainstream political parties to form a loose alliance against the king, said his statement underlined the autocracy of the royalist regime.
"This message has exposed the insensitivity and arrogance of the feudal rulers to the burning issues of the country and its people," rebel chief Prachanda said in a statement.
Arbour: Nepal's participation in
peacekeeping missions is at risk
"Our party urges the people to turn the new year into a year of freedom from the feudal autocratic regime."
In his message, the 58-year-old monarch made no reference to the mass campaign against his rule, which has brought the impoverished country, wedged between India and China, to a standstill.
He also made no mention of Maoist rebels.
More than 13,000 people have been killed in the Maoist revolt which has wrecked the aid and tourism dependent economy.
In New York, Louise Arbour, the UN high commissioner for human rights, said she was shocked by the "excessive" use of force by Nepal's security forces against pro-democracy protesters, warning the government its participation in UN peacekeeping missions could be affected.
The royalist government in Kathmandu was quick to react.
Shirish Shamsher Rana, the information minister, said: "Whatever pontification the West is giving about democracy to the king, it should be directed at the political parties."
"My king does not make mistakes. The king listens to his people. Why don't the political parties listen to the people?"