On Wednesday, both Democratic and Republican senators said they expect the Senate to vote on the issue.
"You will see war powers resolutions regarding Cuba, Mexico, Colombia, Nigeria and Greenland," Democratic Senator Tim Kaine said at a press conference.
Kaine has led several resolutions aimed at limiting presidential use of military power without congressional approval.
According to the White House, President Donald Trump is "actively" discussing buying Greenland with his staff.
Next week, U.S. Secretary of State Marco Rubio will meet with representatives from Denmark to discuss developments regarding Greenland, according to Rubio. Greenlandic representatives will also participate.
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