Last month Christians were prevented from burying their dead in the grounds of the Hindu Pashupatinath Temple - which they have done for decades.
They say that there are only a few places where they can bury their dead in predominantly Hindu Nepal.
The government has pledged to find land near Kathmandu for Christian burials.
So far no progress has been made in resolving the issue. Temple authorities have said that there is no space left for new graves.
Most bodies in Nepal are cremated in keeping with Hindu tradition.
The BBC's Joanna Jolly in Kathmandu says that Christianity is a growing religion in Nepal - where it has become popular among low-caste Hindus as a way of escaping the rigid caste system.
About 1,000 Christians attended the protest in the centre of Kathmandu, some carrying banners which read "Give us our rights, give us burial grounds".
Pastor Sundar Thapa - who led the protest - said the Christian community wanted the government to provide space in all 75 districts of the country so that "we can bury our dead according to Christian practices".
"If the government listens to our demands, we will [continue] peacefully living in this country and helping this country to develop. But if it doesn't listen, then we will have to come on to the streets in coming days," he said.
Some Christians have warned that if the government does not provide the land, they will even go so far as to parade their dead in front of parliament.
The Supreme Court temporarily lifted the Pashupatinath temple ban, but the dispute continues and Christians have been protesting since it was announced.
Christian leaders have also been demanding that the government formally recognise their status.
Hindus make up the majority of the population in Nepal - Christians comprise about 1.5% of the country's 27 million people.
© Kieron Nelson 2011 "Vanishing Cultures Photography"