"There's been no impact on my work at the military level up to this point... I would just say that we're ready to defend every inch of alliance territory still today," Grynkewich told reporters during a visit to Finland.
"So I see us as far from being in a crisis right now," he added.
Grynkewich's comments followed Trump repeatedly stating that he wants US control of the mineral-rich autonomous Danish territory.
President Trump has not ruled out the use of military force to acquire the strategically located Arctic island with a population of 57,000 people.
In an interview with The New York Times published Thursday, President Trump was asked if his priority was preserving the NATO military alliance or acquiring Greenland, and he told the newspaper: "It may be a choice."
Asked by a reporter about Trump's statement, Grynkewich said he did not wish to comment on whether NATO would survive without the US.
Trump has long talked about acquiring Greenland but has ramped up his threats since the US military operation to topple Venezuela's ruler Nicolas Maduro last week.
US Secretary of State Marco Rubio is due to meet officials from Denmark and Greenland next week.
Washington already has a military presence in Greenland -- the Pituffik base, which dates from World War II when the United States sent forces to defend Greenland after Denmark fell to Nazi Germany.
Some 150 personnel are permanently stationed at the base, but the United States stationed up to 6,000 troops across Greenland during the Cold War, largely out of concerns that any Soviet missile would cross the island on its way to North America.
Under a 1951 treaty, the United States could simply notify Denmark it is again sending more troops.
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