Accounts that changed their name to Elon Musk and mocked the billionaire have already been suspended.
Several accounts that had changed their name to the new Twitter owner have been suspended or placed behind a warning sign, including those of US comedian Kathy Griffin and former NFL player Chris Kluwe.
Mr Musk has previously said he opposed permanent bans on Twitter, including that of Mr Trump's official account. Mr Musk said last week that banned accounts would not be reinstated until there was "a clear process for doing so". He pointed out that he was not banning an account that followed his private plane.
On Friday, the billionaire said Twitter was losing more than $4m per day, insisting that this gave him "no choice" over culling around half the company's 7,500-strong workforce.
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