In 1950, Alan Turing, the gifted British mathematician and code-breaker, published an academic paper. His aim, he wrote, was to consider the question, “Can machines think?”

The answer runs to almost 12,000 words. But it ends succinctly: “We can only see a short distance ahead,” Mr. Turing wrote, “but we can see plenty there that needs to be done.”

More than seven decades on, that sentiment sums up the mood of many policymakers, researchers and tech leaders attending Britain’s A.I. Safety Summit on Wednesday, which Prime Minister Rishi Sunak hopes will position the country as a leader in the global race to harness and regulate artificial intelligence.

On Wednesday morning, his government released a document called the Bletchley Declaration, signed by representatives from the 28 countries attending the event, including the U.S. and China, which warned of the dangers posed by the most advanced “frontier” A.I. systems.

“There is potential for serious, even catastrophic, harm, either deliberate or unintentional, stemming from the most significant capabilities of these A.I. models,” the declaration said.

“Many risks arising from A.I. are inherently international in nature, and so are best addressed through international cooperation. We resolve to work together in an inclusive manner to ensure human-centric, trustworthy and responsible A.I.”

The two-day summit in Britain is at Bletchley Park, a countryside estate 50 miles north of London, where Mr. Turing helped crack the Enigma code used by the Nazis during World War II. Considered one of the birthplaces of modern computing, the location is a conscious nod to the prime minister’s hopes that Britain could be at the center of another world-leading initiative.

Bletchley is “evocative in that it captures a very defining moment in time, where great leadership was required from government but also a moment when computing was front and center,” said Ian Hogarth, a tech entrepreneur and investor who was appointed by Mr. Sunak to lead the government’s task force on A.I. risk, and who helped organize the summit. “We need to come together and agree on a wise way forward.”

With Elon Musk and other tech executives in the audience, King Charles III delivered a video address in the opening session, recorded at Buckingham Palace before he departed for a state visit to Kenya this week. “We are witnessing one of the greatest technological leaps in the history of human endeavor,” he said. “There is a clear imperative to ensure that this rapidly evolving technology remains safe and secure.”

Vice President Kamala Harris, and Gina Raimondo, the secretary of commerce, were taking part in meetings on behalf of the United States.

Wu Zhaohui, China’s vice minister of science and technology, told attendees that Beijing was willing to “enhance dialogue and communication” with other countries about A.I. safety. China is developing its own initiative for A.I. governance, he said, adding that the technology is “uncertain, unexplainable and lacks transparency.”

In a speech on Friday, Mr. Sunak addressed criticism he had received from China hawks over the attendance of a delegation from Beijing. “Yes — we’ve invited China,” he said. “I know there are some who will say they should have been excluded. But there can be no serious strategy for A.I. without at least trying to engage all of the world’s leading A.I. powers.”