Trump is the Republican presidential candidate in the Nov. 5 US election.
While Trump's Twitter posts are publicly viewable, X also holds non-public information on accounts like direct messages, drafts of social media posts, location data and the type of device used to send posts.
It was not clear whether Smith's prosecution of Trump has relied on information gleaned from the Twitter account.
In Smith's August 2023 indictment, Trump was charged with conspiring to defraud the United States, corruptly obstructing an official proceeding and conspiring to do so, and conspiring against the right of Americans to vote.
In January 2023, US District Judge Beryl Howell approved Smith's request for a search warrant directing X to produce records related to Trump's Twitter account. The Washington-based judge also barred X from notifying the former president about the warrant, finding "reasonable grounds to believe" that disclosing the warrant to Trump "would seriously jeopardize the ongoing investigation" by giving him "an opportunity to destroy evidence, change patterns of behavior, (or) notify confederates."
Lawyers for X argued that the nondisclosure order violated the company's right to communicate with Trump, its subscriber, citing the First Amendment protections.
X also argued that Howell should have ruled on its First Amendment challenge before allowing prosecutors to execute the warrant in order to preserve any potential claims by Trump involving executive privilege. This legal principle allows certain records to be shielded from lawmakers and the courts to protect the ability of presidents to obtain candid advice on major decisions.
X initially resisted complying with the warrant and was held in contempt of court and fined $350,000 before producing Trump's records to the special counsel in February 2023.
On appeal, the US Court of Appeals for the District of Columbia Circuit in August 2023 upheld Howell's decisions, prompting X's appeal to the Supreme Court.
X's legal team asked the justices to review its First Amendment challenge to Howell's nondisclosure order, as well as the judge's refusal to resolve the company's constitutional objections before the warrant was executed.
In response, Smith urged the justices to reject X's appeal, arguing that the company's claims were without merit and that the case is moot because prosecutors have already obtained Trump's Twitter account information.
The social media platform, still called Twitter at the time, suspended Trump's account in January 2021 - citing the risk of further incitement of violence following the storming of the U.S. Capitol by his supporters - but reversed its position under Musk, who has called himself a "free speech absolutist."
Musk has endorsed Trump in the presidential election. Trump has said that, if elected, he would establish a government efficiency commission headed by Musk.