San Francisco, California - Elon Musk's takeover of Twitter is causing big trouble even before being actually completed.

The former CEO of the platform has accused Musk of making one senior executive a "target of harassment and threats."

Dick Costolo used Twitter to respond to a meme posted by Musk featuring Vijaya Gadde.

The Tesla boss appeared to be using Gadde – Twitter's head of legal, policy, and trust – to suggest the company had a "left-wing bias."

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Costola, who was the chief executive of the tech giant between 2010 and 2015, replied to Musk: "What's going on? You're making an executive at the company you just bought the target of harassment and threats."

In a subsequent tweet, the former Twitter boss wrote: "Bullying is not leadership."

Musk hit back: "What are talking about? I'm just saying Twitter needs to be politically neutral."

He then added: "For Twitter to deserve public trust, it must be politically neutral, which effectively means upsetting the far right and the far left equally."

The current CEO of the company also posted to the platform, appearing to show solidarity with the website's employees who have been the subject of criticism by Musk in recent days.

Parag Agrawal said he was proud of "our people" who managed to stay focused despite the "noise".

"I took this job to change Twitter for the better, course correct where we need to, and strengthen the service," the software engineer wrote. "Proud of our people who continue to do the work with focus and urgency despite the noise."

Musk's personal use of the platform is attracting increased criticism as he continues to use it to publicly question policy decisions made by Gadde, who has seen her account flooded with abuse.

The latest controversy came just hours after the chairman of the Joint Committee on the draft Online Safety Bill urged Musk to "clean up" the site.

Gadde, who has worked at Twitter since 2011, is the key executive charged with overseeing Twitter's trust and safety, legal, and public policy functions. Her decision to remove all political advertising and to boot former President Donald Trump from Twitter in the wake of the January 6 Capitol attack made her the target of a large contingent of right-wing critics.

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The public spat between Twitter's former CEO and Musk comes after a senior figure at the company said it is "weird to process" his multibillion-dollar takeover of the social media platform.

News of the $43.25-billion takeover this week prompted some to question the future safety of the platform and saw some users threaten to leave.

While Twitter founder Jack Dorsey has hailed the decision to let Musk take the social media platform into private ownership, away from the ad model and Wall Street, others have raised concerns about online safety going forward given the Tesla and SpaceX chief executive's belief in absolute free speech – although that's not a principle he's always stuck to in practice.

Twitter's senior director of global public policy, Nick Pickles, said he was "still processing" what had happened, but insisted that in the end, "the service is what matters."