The Cherokee Nation wants Jeep to stop using its name to sell the firm's classic sports utility vehicles.
Cherokee Nation Principal Chief Chuck Hoskin Jr said "it's time" for companies and sports teams to retire Native American iconography from logos, mascots and other products.
Jeep has sold vehicles under the name since the 1970s. The current make is one of its most popular vehicles.
It said the name had been "carefully chosen", but was committed to dialogue.
"Our vehicle names have been carefully chosen and nurtured over the years to honour and celebrate Native American people for their nobility, prowess and pride," the company said in a statement.
"We are, more than ever, committed to a respectful and open dialogue with Cherokee Nation Principal Chief Chuck Hoskin Jr."
'It does not honour us'
Jeep, which is owned by multinational Stellantis after the merger of Fiat Chrysler and PSA Group, is one of many corporations under pressure to update branding.
Amid widespread Black Lives Matter protests last summer, food companies such as PepsiCo said they would overhaul certain products, after criticism that its brands relied on racist tropes. Some sports teams have also announced changes.
"I think we're in a day and age in this country where it's time for both corporations and team sports to retire the use of Native American names, images and mascots from their products, team jerseys and sports in general," Mr Hoskin said in a statement.
"I'm sure this comes from a place that is well-intended, but it does not honour us by having our name plastered on the side of a car."
He made the initial comment in an interview with trade magazine Car and Driver.
Native American imagery has been used in the US for decades to promote everything from cigars and butter to cars like the Cherokee, Pontiac and Winnebago.
A 2018 exhibition at the Smithsonian's National Museum of the American Indian in Washington had a section dubbed simply "Indians are Everywhere".
Jeep reintroduced the Cherokee name to the US market in 2013, after temporarily dropping it roughly a decade earlier. It has announced plans to unveil an all-electric Jeep Cherokee later this year.
In 2013, the Cherokee Nation told the New York Times it had not been consulted and was opposed to stereotypes, but did not have an institutional stance on the matter.