Police used tear gas and beat protesters with batons to break up rallies in the Kalanki and Dhumbarahi areas of the capital on Monday.
About 1,500 people were reported to have blocked the streets in the Kirtipur area of Kathmandhu, singing pro-democracy songs while the security forces watched without intervening.
Hundreds of flag-waving marchers also defied a curfew imposed in the west Nepal town of Pokhara.
Krishna Prasad Bhandari, a 17-year-old Kathmandu activist, said: "We will establish a democratic republic soon. I think the king will melt if we continue protests like this for another 15 days. Otherwise he is not going to relent."
Three demonstrators have been reported killed and 800 arrested in the past five days of protests against King Gyanendra's direct rule.
The authorities imposed a daytime curfew around the Kathmandu area for a third consecutive day on Monday.
The protests, backed by a general strike, had been due to end on Monday, but opposition parties said they were extending them indefinitely to put pressure on the king to end his rule.
The royal government has threatened to use more force to end the protests, saying that Maoist rebels have infiltrated them.
Nepal has been in a political emergency since King Gyanendra sacked the government and seized power in February 2005.
The king says that he took power because of the growing Maoist insurgency, which has killed nearly 13,000 people since 1996.