|T-shirts denouncing halal products were worn by people at the rally|
Thousands of supporters of the group attended a rally in a suburb of the capital, Colombo.
The calls come at a time of mounting religious tension in the country.
There have been several attacks on both mosques and Muslim-owned businesses as well as on Christian churches and the clergy, the BBC's Charles Haviland reports from Colombo.
Thousands of men and women filled the grounds of the rally and the surrounding streets at Maharagama in Colombo's outer suburbs to hear nationalist speeches by the group's monks.
The leaders called for a boycott of halal meat and demanded shops clear their stocks by April, the AFP news agency reports.
Youth activists at the rally wore T-shirts denouncing the Muslim halal method of slaughtering animals to eat.
The group's secretary-general, Venerable Galaboda Aththe Gnanasara, told the crowds that "only monks can save this race", referring to Sinhalese.
He claimed that Christian and Muslim extremists were threatening Buddhists, and said hundreds of monks were ready to fight. "Our country is a Sinhalese one and we are its unofficial police," he said.
The group has denied being anti-minority, and has dissociated itself from the recent attacks on Muslim and Christian targets.
But one member of the group, Dilanthe Withanage, accused "some" unnamed countries of "funding Christian fundamentalists as well as Muslim fundamentalists" in Sri Lanka.
Both Muslims and Christians deny promoting extremism in Sri Lanka, our correspondent reports.
President Mahinda Rajapakse has called on monks not to incite religious hatred and violence, but one opposition politician told the BBC that "the situation is very bad".
"Any moment, the ethnic riot will start between Sinhalese and Muslims," said Mujeebur Rahuman of the opposition United National Party.
"They are now working freely. Nobody is talking about this organisation and the government is not trying to stop their activities."
The Buddhist Sinhalese make up three-quarters of Sri Lanka's 20 million population.
Muslims constitute about 10% and have generally had good relations with the Sinhalese majority.