While the main protest on Thursday was not stopped by security forces, who were heavily deployed across the city, police had earlier fired tear gas to disperse two dozen students protesting against the king's rule at the Amrit Science College near the royal palace on Thursday morning.
No arrests or injuries were reported there.
The elections on Wednesday were for the relatively powerless posts of mayors and local council members, and the dearth of voters at the polls was considered a serious blow to the
rule of King Gyanendra, who seized power a year ago.
More than 4000 demonstrators swept into Kathmandu's city centre early on Thursday afternoon, waving banners, shouting slogans and calling for punishment for the soldiers who killed a
protester on the day of the vote.
"Hang the culprits! Down with autocracy! We will fight for democracy," some chanted.
In initial returns for 15 of the 36 cities and towns where polls were held, the pro-government Rastriya Prajatantra Party won 10 mayoralties, the pro-government Nepal Sadbhawana won two and independent candidates won three, the Election Commission said.
Six people were killed in violence on election day, including a protester shot by soldiers during the vote, which the US called "a hollow attempt" by King Gyanendra to solidify power.
An international election observer said the vote had a number of flaws.
The country's seven main parties
shunned Wednesday's election
The country's seven main political parties shunned the elections to protest against what they called the king's power grab, which he said was needed to bring the country's Maoist insurgency under control.
However, rebel attacks have intensified in recent weeks.
Krishna Sitaula of the Nepali Congress party said: "We refuse to accept the results from these so-called elections.
"We will not accept [the winners] as representatives of the people and will not allow them to take their positions."
Keshav Raj Rajbhandari, the chief election commissioner, said turnout was estimated at over 20% but that the final figure was still being tabulated.
Three insurgents, a policeman and a civilian were killed in two separate election-day rebel attacks, one in eastern Nepal and the other in the west, the police and Defence Ministry said.
The royal government rounded up hundreds of politicians, activists and journalists in the weeks before the elections.
On Wednesday morning, police arrested about 30 politicians and activists who were trying to organise protests in an eastern border town.