The US Justice Department filed papers late on Friday, seeking reconsideration of the case by 2nd US Circuit Court of Appeals in New York, CNN reported.
The 2nd US Circuit Court of Appeals is yet to confirm whether it would rehear the case.
In July, a three-judge panel decided that blocking Twitter users from following or interacting with the account of the US President (@realDonaldTrump) amounted to violating the US Constitution.
The US Justice Department argues that Trump should be able to block users on the microblogging platform as it is his personal account which will be in use even after he leaves office.
Trump is an avid Twitter user and he often uses the platform to make important announcements.
And because it is used for government business, the appeals court previously held that the handle is a public forum.
The appeals court upheld a lower court ruling in the case of Knight First Amendment Institute versus Trump that the President's Twitter account constituted a "public forum."
The appeals court said its ruling was based on the principles in the US Constitution's First Amendment, which protects freedom of expression.
"We do conclude, however, that the First Amendment does not permit a public official who utilises a social media account for all manner of official purposes to exclude persons from an otherwise-open online dialogue because they expressed views with which the official disagrees," Judge Barrington D. Parker wrote in the decision.
The appeals panel said that the government and its officials had to allow differing points of view to be expressed.
( With inputs from IANS )