Lawyers for Trump, a Republican, told the San Francisco-based 9th U.S. Circuit Court of Appeals in a filing that the ban from Twitter marked "overtly partisan censorship" and was "contrary to First Amendment principles deeply rooted in American history and law."
His lawsuit seeks compensatory and punitive damages and a court order requiring Twitter to "immediately reinstate" his account that was permanently suspended on Jan. 8, 2021.
Trump has vowed to keep posting to his own Truth Social media platform. Twitter's new owner, billionaire Elon Musk, has said that he would reinstate Trump's account.
A spokesperson for Trump did not immediately respond to a message seeking comment, and a Twitter spokesperson did not immediately reply.
A lawyer for Trump, John Coale in Washington, told Reuters on Monday, "We want him to have the right to get back on" to Twitter.
Twitter said last year it had permanently suspended Trump's account "due to the risk of further incitement of violence" after his supporters stormed the U.S. Capitol as it was preparing to certify Democrat Joe Biden's presidential win.
San Francisco-based U.S. District Judge James Donato in May dismissed Trump's claim that his ban from Twitter violated speech protections accorded under the U.S. Constitution's First Amendment.
Donato also denied Trump's claim that Twitter was serving as a "state actor" when it banned his account.