The Trump-Musk political marriage blew up on Thursday as the president declared himself "very disappointed" in criticisms from his former aide and top donor -- before the pair hurled insults at each other on social media.
At the commission's daily briefing, spokesperson Paula Pinho was asked whether Musk had reached out to the European Union with a view to relocating his businesses, or setting up new ones.
"He's very welcome," she replied with a smile.
The commission's spokesperson for tech matters, Thomas Regnier, followed up by stressing -- straight-faced -- that "everyone is very welcome indeed to start and to scale in the EU".
"That is precisely the objective of Choose Europe," he said, referencing an EU initiative in favour of start-ups and expanding businesses.
Musk has been a frequent critic of the 27-nation EU -- attacking its digital laws as censorship and berating its leaders, while cheering on the ascendant far-right in Germany and elsewhere.
The tycoon's row with Trump saw the president threaten to strip him of government contracts estimated at $18 billion -- with Musk vowing in response to end a critical US spaceship programme.
Explaining the rift, Trump said Musk had gone "crazy" about a plan to end electric vehicle subsidies in the new US spending bill -- as the bust-up sent shares in Musk's Tesla car company plunging.
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