More than 500 people staged a sit-in protest on the outskirts of the capital against Gyanendra, who dismissed the elected government early this year, claiming he needed full executive powers to put down a Maoist rebellion.
The 12-hour protest was staged by human rights groups, political activists and journalists on a highway near Kathmandu's airport, witnesses said.
Jail authorities, meanwhile, freed newly-pardoned prisoners across the country, according to Nepal's state-owned news agency RSS.
The constitution came into being in 1990 with the re-establishment of multi-party democracy after 30 years of the party-less Panchayat system, which collapsed following political protests.
The king dismissed the government in February, earning him international condemnation and a suspension of arms sales from India and Britain.
In a message to the nation marking Constitution Day, Gyanendra said the right atmosphere had been created for elections to be held soon. "It is a matter of satisfaction for all those who have faith in democracy that ... a conducive environment has been created in the last eight months to initiate the process of free and fair elections, ensuring a meaningful exercise in democracy," RSS quoted him as saying.