The opening is a clear French signal against US pressure to take over the island.
"It is a political signal, linked to a desire to be more present in Greenland, including scientifically," Barrot said on French television, according to the AFP news agency.
"Greenland does not want to be owned, governed... or integrated into the United States. Greenland has chosen Denmark, NATO and the (European) Union," Barrot said.
The promise of a consulate was made earlier this summer when President Emmanuel Macron visited the island.
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