But the most geopolitically important — and controversial — symbol of embrace came Saturday, when Italy formally agreed to be part of China’s signature foreign policy and infrastructure project, known as the Belt and Road Initiative, becoming the first Group of Seven country to do so.

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At a ceremony at a Renaissance villa that also included the signing of other business and commercial agreements, Italian Prime Minister Giuseppe Conte said his country was building a “more effective relationship” with China.

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Italy, whose economy has sagged for decades, says the potential economic benefits are too great to pass up. But in pursuing the Belt and Road deal, Italy’s populist government is breaking ranks with the most powerful countries of the West, defying the wishes of the Trump administration, and highlighting the unsettled debate within Europe on how to deal with China’s globally expanding ambitions.

That question is playing out in Europe with increased urgency amid an intense trade dispute between Beijing and Washington. The United States has depicted China as a rule-breaker intent on stealing technology, disrupting the international order and threatening nations’ security with its next-generation telecommunications equipment. Much of Western Europe, too, has grown more cautious about Chinese investment, and earlier this month, the European Commission, in notably blunt language, described China as a “systemic rival.”

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China, with its Belt and Road Initiative — a vast multicontinent project of highways, rail lines and energy pipelines — has been trying to expand its reach closer to the heart of Europe. Other European Union countries, mostly in the continent’s east, have already signed on to the project. However, diplomatic analysts say the involvement of Italy, a founding E.U. member, gives the project a particular boost of legitimacy. The deal would open the door for Chinese infrastructure investment in Italian ports, while making it easier for Beijing to gain influence and trade goods in Western Europe.

Italian leaders have said they are simply doing what is economically prudent for their country, which is in the middle of its third recession in a decade. Deputy Prime Minister Luigi Di Maio said Italian companies will gain much-needed market access in China, and Conte said the deal with China does not jeopardize Italy’s place in the euro-Atlantic alliance.

“A new Silk Road,” Conte said, in a reference to the ancient trade routes that centuries ago helped to enrich Italian traders and foster a maritime empire around Venice.

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“We export a lot less than we import, compared with our European friends,” said Licia Mattioli, vice president for international affairs at Confindustria, the main Italian industry association. “So we think there is a huge potential that we can exploit.”

Officials in Washington have warned that Italy is making a mistake and overlooking the downsides of doing business with Beijing. Criticism of the Belt and Road projects has been extensive. In some countries, the Chinese infrastructure projects have been beset by cost overruns. China helps to finance the projects, but in smaller countries, the setup can leave governments owing enormous sums to Beijing relative to their GDP. Above all, some experts are concerned China is building an infrastructure empire as a way to upend security and the economic world order.

Garrett Marquis, spokesman for the White House National Security Council, said earlier this month that the Italian government had no need to “lend legitimacy to China’s infrastructure vanity project.” In an usually blunt critique of an ally, the Security Council’s official Twitter account also took aim at Italy, calling China’s approach “predatory” and saying the deal “will bring no benefits to the Italian people.”

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The Italian government, composed of two anti-establishment parties, has shown a willingness over the past year to go its own way on major decisions. But Francesco Sisci, an Italian professor at People’s University of China, said the timing of the decision — amid a trade war and growing E.U. debate about how to handle China — makes the move more fraught.

“Italy should have had extensive consultations with both the U.S. and Europe,” said Sisci, who emphasized his views did not reflect those of his university in Beijing. “Not to go in a way behind their backs.”

French President Emmanuel Macron has urged a more cautious approach to the Belt and Road Initiative, saying partner countries risked becoming “vassal states.” After leaving Italy, Xi is spending several more days in Europe, traveling first to Monaco and then to France, where he will meet with Macron and German Chancellor Angela Merkel.

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Both France and Germany have taken more guarded stances against China, but even they have not gone as far as the United States would like.

The Trump administration has sought to convince European capitals to ban Huawei, the Chinese telecom giant, from their 5G next-generation telecom networks, concerned that the company could use its technology for spying purposes.

So far, however, U.S. warnings have gone largely unheeded. Merkel said Tuesday that she does not believe in excluding a company “simply because it’s from a certain country.”

Two weeks ago, Huawei opened a cybersecurity lab in Brussels, and the E.U. headquarters there will host an E.U.-China summit next month to be attended by Chinese Premier Li Keqiang.

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Within Italy’s government, one coalition member, the right-wing League, expressed more skepticism about the deal with China. The League’s leader, Matteo Salvini, had said he would try to halt the deal if it looked like it might jeopardize national security. Massimiliano Romeo and Riccardo Molinari, two of the League’s leaders in Parliament, issued a joint statement saying that, while it is important that Italian companies have the chance to grow, “when national security and sovereignty are at stake, great prudence is required.”

“We are friends of everyone, nobody’s colony,” they said.