The Trump administration says it wants American AI to dominate the world.But its decision to force Anthropic to abruptly cut off access to one of its most advanced models risks sending foreign governments and companies a very different message: Don't build your future on U.S. AI.Why it matters: As the Trump administration shapes its AI regulatory regime in real time, the precedents it sets could reverberate far beyond an individual showdown with Anthropic.Catch up quick: The last month of AI policymaking has been a blur of zigs and zags by the administration.First Trump delayed an executive order that would have created a voluntary reporting system for advanced AI releases. He said he didn't want to threaten America's lead over China. A few weeks later, the White House issued a slimmed-down executive order that explicitly barred mandatory government licensing.Then came Friday: The administration placed Anthropic's Mythos 5 and Fable 5 under export controls, a move critics said amounts to a licensing system by another name.Driving the news: The move against Anthropic — which came as the Pentagon is already tangling with the company — has some foreign governments doubting they can depend on U.S. AI."The situation we're in collectively right now with Mythos and Fable is something that can happen with overreliance on certain models," Canadian Prime Minister Mark Carney said Sunday. "You'll hear me say this over and over again. It is never a good idea to have one option," Carney said.Early this month, the European Union launched a "tech sovereignty" initiative to reduce dependence on foreign technology providers, including American AI and cloud companies. It wants to dramatically expand data center and semiconductor production.""Europe wants to be in the position to make its own choices, avoiding risky dependencies on single dominant suppliers, one company or one third country," European Commission Executive Vice-President Henna Virkkunen, who oversees tech sovereignty, told reporters.Friction point: The risk is that foreign governments and companies will look elsewhere if they come to view American AI as unreliable. Google DeepMind CEO Demis Hassabis said in January that China is roughly six months behind the U.S. when it comes to frontier, or leading, AI."For some applications, Chinese models will be an attractive back-up, especially when they are open-sourced and so can be used with relatively little risk," Anton Leicht, an AI expert at the Carnegie Endowment for International Peace, tells Axios.Yes, but: Overall, no other country — including China — is close enough to the U.S. in data center buildout or chip production to give the Trump administration second thoughts, Leicht added.What they're saying: Gartner noted in a Monday report that this was the first time that a government has intervened to block access to an AI model customers were already using — and warned it probably won't be the last."Operational risk can stem not just from a vendor's performance but also from unpredictable government interventions," the technology research firm said."The Trump administration is collaborating with AI industry leaders to balance cutting-edge innovation with national security concerns that affect both the United States and our allies," White House spokesman Kush Desai said. "The United States is by far the world leader in the global AI race, and President Trump is committed to ensuring America's technological dominance."The bottom line: The Trump administration is sending mixed signals about its approach to AI regulation — and it's giving allies abroad the jitters.