'Aggressive move'
"It should be said clearly that our integrity and democracy must be respected without foreign interference," Egede said in a post on Facebook.
He added that the US delegation's visit "cannot be seen as just a private visit".
"(Waltz) is Trump's confidant and closest advisor, and his presence in Greenland alone will certainly make the Americans believe in Trump's mission, and the pressure will increase after the visit," Egede told Sermitsiaq.
Ulrik Pram Gad of the Danish Institute for International Studies called the visit an "aggressive move" by Washington.
"They haven't been invited by Greenlanders. They haven't been invited by the Danes. They just announced that they will go," he told AFP.
Greenland's political parties are currently in the process of negotiating a new coalition government following the election, which the center-right Democrats won.
"Normally, as a friend or ally, you would stay out of that," Pram Gad said.
Jens-Frederik Nielsen -- leader of the Democrats and likely future Greenlandic prime minister -- has previously criticised Trump's Greenland ambitions as "inappropriate".
On Monday, Nielsen stressed that ongoing negotiations for a new coalition government following the election were continuing and that they would not let themselves "be pressured".
Pram Gad said that, with no officials to welcome the US delegation, "they will be pushing this point that 'OK, nobody's in control here, there's a need for us to step in'," he said.
He said the choice to send Usha Vance was part of a "sham" charm offensive while the inclusion of Chris Wright "sends the signal that we're after resources here".