New York (CNN) The Justice Department and a group of Twitter users faced off Tuesday in the appeal of a case over whether President Donald Trump's blocking of certain accounts violates the First Amendment.

Before a three-judge panel in Manhattan federal court, the Justice Department argued that Trump wasn't "wielding the power" of the federal government when he blocked certain individuals from his personal Twitter account, @realDonaldTrump, because while the President sends tweets in his official capacity, he blocks users as a personal matter.

But an attorney for the Knight First Amendment Institute -- which, along with seven individuals who have been blocked by the President on Twitter, sued Trump last year -- said the President's actions were taken in his official government capacity.

Though conceding that Trump had launched the account before he took office, the attorney, Jameel Jaffer, said Trump "began using it as President as an extension of his office."

Though the panel didn't rule on the matter, the judges appeared to question the Justice Department's argument. If Trump blocked people in his personal capacity, "it is curious to me that the Justice Department is here representing him," Judge Peter Hall said in response to the government's attorney, Jennifer Utrecht.

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