"I don't quite know why we're here", Buchwald told lawyers from the Department of Justice and the Knight Institute Thursday morning.
"What we're seeking is having President Trump stop blocking our plaintiffs and stop blocking people because of viewpoint", she said.
The lawsuit was filed against Trump in July by the Knight First Amendment Institute at Columbia University and several Twitter users.
Buchwald kept coming back to muting as a compromise that wouldn't give critics equal access to the president through Twitter and wouldn't let Trump keep them completely away from his account, but would give both sides part of what they wanted.
During the hearing, Judge Buchwald asked Trump's lawyer, Michael Baer, if Twitter was any different from a town hall meeting.
But Buchwald was clearly serious about the proposal; as the two-hour hearing reached its close early Thursday afternoon, the judge urged the two sides to "consider my earlier suggestion".
Plaintiffs in the case blocked by the president include political consultant Rebecca Buckwalter, University of Maryland sociology professor Philip Cohen, Grammy-nominated songwriter Holly Figueroa, Vanderbilt University surgeon Eugene Gu, former Guantanamo Bay prison guard Brandon Neely, retired cyclist Joseph Papp and comedy writer Nicholas Pappas. Buchwald said. "He can avoid hearing them by muting them". "I don't think it's a ideal solution, but it's far less restrictive", Fallow said.
Over March, May, and June 2017, the President blocked the seven accounts, which tweeted critical comments of the President and his policies. It was never my point.
The White House did not return a request for comment but has said in the past that it does not comment on pending litigation. "He wants to look out at the world on Twitter and see that everyone agrees with him and everybody thinks he's great and the fact is that's not true and that's why he blocks - just literally blocks - us so we won't be seen to be expressing our views against him, and I think that's outrageous".
"Once it is a public forum, you can't shut somebody up because you don't like what they're saying", said Reice.
Moreover, Baer noted that all but one of the plaintiffs has continued to engage the president's tweets despite being blocked by him. This feature helps users in restricting specific accounts from contacting them, seeing their tweets, and following them.
To deny some Twitter users the ability to view and reply to these tweets is to deny their First Amendment right, the Knight Institute contends. This has barred these users from interacting with the President's @realdonaldtrump account.