President Biden was set to meet with Prime Minister Rishi Sunak of Britain at the White House on Thursday to discuss economic cooperation, the rise of artificial intelligence and the war in Ukraine.

Mr. Biden and Mr. Sunak have met several times at diplomatic events in recent months, but the prime minister’s two-day visit to Washington is a high-profile engagement, including a bilateral meeting and a planned afternoon news conference.

Mr. Sunak, who is 43 and has been in office since October, is under pressure to establish post-Brexit Britain as a competent and reliable global player. He is looking to strengthen economic ties in the West in part to counter shared foes, such as China, as he noted ahead of the meeting.

“Just as interoperability between our militaries has given us a battlefield advantage over our adversaries,” he said, “greater economic interoperability will give us a crucial edge in the decades ahead.”

Mr. Sunak is concerned about issues raised by A.I., a field in which developments are happening faster than the efforts to regulate them. He is likely to also discuss other business matters with Mr. Biden, including potentially reaching a modest agreement around critical minerals for electric vehicles, similar to one the United States reached with Japan in March.

Though economic concerns are at the top of Mr. Sunak’s agenda, the uptick in fighting between Ukrainian and Russian forces in recent days, as well as the destruction of a major dam on the Dnipro River in southern Ukraine on Tuesday, is likely to consume much of the conversation between the leaders.

Mr. Sunak, like Mr. Biden, has been a vocal supporter of Kyiv. He told reporters on his flight to Washington that if Moscow was behind the attack, it would constitute “the largest attack on civilian infrastructure in Ukraine since the start of the war, and just would demonstrate the new lows that we would have seen from Russian aggression.”

American military officials have watched with resignation as the fighting intensifies in Europe, and Mr. Biden, who had no public events on his schedule on Wednesday, has reaffirmed his continued support for Kyiv.

“We are not leaving,” he told reporters at the White House on Tuesday. “We’re going to help Ukraine.”

Despite their political differences — Mr. Biden is a moderate liberal and Mr. Sunak is conservative — the meeting on Thursday will be an opportunity for both men to display a shared leadership style that emphasizes even-keeled diplomacy.

Mr. Biden has spent much of his time in office seeking to stabilize the United States’s relationship with allies around the world in the wake of the Trump presidency. And Mr. Sunak, who ascended to power after the bombastic tenure of Boris Johnson and the very brief one of Liz Truss, has sought to establish himself as a more dependable occupant of 10 Downing Street. Both have low approval ratings, and both lead countries that have so far managed to avoid economic recession but whose voters feel financially constrained by inflation.

“The economy will be part of that conversation,” Karine Jean-Pierre, the White House press secretary, told reporters on Wednesday. “They have one of the strongest, largest bilateral investment relationships in the world.”