The debate over Columbus's legacy is an old one, but it has become emotionally charged after a similar debate in the USA over monuments to Confederate generals turned deadly at a rally in Charlottesville, Virginia in August.
One attempt to dump Columbus Day in Akron, Ohio, opened a racial rift on the city council.
A statue of Columbus was defaced in New York City's Central Park in September with the words "hate will not be tolerated". Activists calling for the city to change the name are expected to hold a demonstration.
The group is meeting Tuesday for the first time and it may debate the fate of statues like the Columbus Circle one.
Two of the three protesters were dressed in fake chains. The New York Police Department says one person was arrested.
While honoring "the skilled navigator and man of faith, whose courageous feat brought together continents", in his first Columbus Day proclamation, President Donald Trump made no mention of Native Americans.
The celebration of Christopher Columbus Day, the Italian explorer credited with discovering America, has faced a backlash over the years because of his maltreatment of Native American populations.
Local people said they supported the committee's decision.
Numerous protesters call for cities and towns to adopt Indigenous People's Day.
The idea of celebrating Indigenous People's Day first was proposed almost 40 years ago, when a delegation of Native nations to a U.N. conference in Geneva passed a resolution. Berkeley, California, got rid of Columbus Day in favour of Indigenous Peoples Day in 1992.
A few cities have compromised.
Austin, Texas followed the Californian city's example, announcing its plans to cease Columbus Day celebrations on Thursday.
But, an advocate for replacing Columbus Day with a day honouring Indigenous people, says the question Americans should ask themselves is whether Columbus is truly a figure who should be celebrated nationwide. "It would lead to the kidnapping, deaths and slavery of tens of millions of African people", said Councilman Russel Neal, who is black.
States and municipalities aren't legally bound to recognize federal holidays, though most do. But he said the nation should "also acknowledge the pain and suffering reflected in the stories of Native Americans who had long resided on this land prior to the arrival of European newcomers".
Columbus Day commemorates the arrival of Columbus in the New World in 1492.