Denmark needs to focus on the fact that Greenlanders do not want to be part of Denmark, US Secretary of State Marco Rubio said on Friday.
"The Greenlanders will make a decision," Rubio told reporters at a news conference after meeting with other NATO foreign ministers in Brussels.
Earlier this week, the Arctic island's new prime minister, Jens-Friedrik Nielsen, announced that he intends to strengthen ties with Denmark until it becomes a sovereign state.
The Danish prime minister landed in Greenland on Wednesday for talks with Nielsen. She said before her visit that she aimed to strengthen Copenhagen's ties with the island and stressed the importance of respectful cooperation amid what she described as "great pressure on Greenland."
A poll in late January found that 85 percent of Greenlanders did not want their Arctic island - a semi-autonomous Danish territory - to become part of the United States.