The video posted by the @TeamTrump account referred to a New York Post story from yesterday that contained alleged details of Hunter Biden's business dealings with a Ukrainian energy company and said the former vice president had met with an adviser of the company.
"Joe Biden is a liar who has been ripping off our country for years," the video was captioned.
Twitter said the video violated its rules against posting private information, adding the account may need to delete the post in order to continue tweeting.
"It's going to all end up in a big lawsuit and there are things that can happen that are very severe that I'd rather not see happen, but it's probably going to have to," Mr Trump said, when asked about the move by Twitter.
Twitter said the Post story violated its "hacked materials" policy, which bars the distribution of content obtained through hacking that contains private information or trade secrets, or puts people at risk of physical harm.
Facebook Inc and Twitter took proactive steps on Wednesday to restrict dissemination of the Post story in the hours after it was published.
Twitter had placed similar restrictions on the account of White House Press secretary Kayleigh McEnany yesterday, after she shared the story.
After Twitter imposed the restrictions, the US Senate Judiciary Committee moved to subpoena Twitter's chief executive Jack Dorsey.
Committee Chairman Lindsey Graham and Republican senators Ted Cruz and Josh Hawley said the Committee will vote on sending the subpoena next Tuesday, October 20th and plans to have Dorsey in front of the committee by October 23rd. -Reuters
