Twitter accepted Elon Musk's offer to buy it on Monday.
Musk has indicated he may loosen Twitter's rules on what content is allowed to stay on the platform.
EU commissioner Thierry Breton warned Musk not to fall afoul of new legislation.
One of the European Union's top lawmakers has issued a warning to Elon Musk over his takeover of Twitter.
Twitter agreed to Elon Musk's offer to buy it for $44 billion on Monday. The billionaire has publicly stated his interest in buying the social media platform is rooted in his idea of "free speech."
Musk has previously described himself as a "free speech absolutist" and his comments have left Twitter staff and others wondering whether he will relax the platform's rules on what content is allowed to stay up.
EU commissioner for the internal market Thierry Breton warned Musk against getting too lax on content moderation in comments to The Financial Times.
Breton told The FT he wanted to give Musk a "reality check" on his plans for more relaxed content moderation.
"We welcome everyone. We are open but on our conditions. At least we know what to tell him: 'Elon, there are rules. You are welcome but these are our rules. It's not your rules which will apply here,'" Breton told The FT.
Breton was one of the driving forces behind the Digital Services Act, a new package of EU legislation that passed Saturday, bringing in stricter laws on how tech giants moderate content on their platforms.
He said Twitter's board will have to meet Europe's laws on issues including moderation, transparency, and hate speech.
Breton said if Twitter fails to comply, the EU could fine the company 6% of its annual revenue or even ban it from operating in Europe entirely.
As well as stipulating how companies police illegal and harmful content, the DSA contains legislation that will force tech companies to open up their algorithms for oversight.
Musk tweeted in the month before he bought the company saying Twitter's algorithm "needs to be open source" — meaning it would be publicly available for scrutiny.
Breton reiterated his warning to Musk in a tweet. "Be it cars or social media, any company operating in Europe needs to comply with our rules – regardless of their shareholding," he said.
"Mr Musk knows this well. He is familiar with European rules on automotive, and will quickly adapt to the Digital Services Act," he added.
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