Biden and Sunak Say Their Countries Will Support Ukraine for the Long Haul

President Biden and Prime Minister Rishi Sunak of Britain affirmed their support for Ukraine on Thursday, pledging to continue drumming up financial and military aid for Kyiv as fighting intensifies on Russia’s front lines.

Mr. Sunak, who made his first visit as prime minister to Washington and is intent on establishing a post-Brexit Britain as a competent and reliable global player, said his country would not turn away from Ukraine. That commitment comes even as both he and Mr. Biden face economic headwinds and domestic concerns about the length of the war.

“There is no point in trying to wait us out,” Mr. Sunak said at a news conference with Mr. Biden in the East Room of the White House, addressing Vladimir V. Putin of Russia, whom he accused of wrongly assuming that the West would tire of providing support. “We will be here as long as it takes.”

Mr. Biden said he was confident that he could persuade a divided Congress to support a new round of funding for Ukraine, though he would not put a dollar amount on the package.

“I believe we’ll have the funding necessary to support Ukraine as long as it takes,” Mr. Biden said, adding that a “vast majority” of his critics in Congress would agree that funding Ukraine would be better than allowing Russia to go unchecked.

Mr. Sunak’s two-day visit was a high-profile engagement for a 43-year-old leader who has held his office only since October and is eager to establish himself on the world stage. It also presented an opportunity for Mr. Biden to deepen his relationship with a young leader who is keenly aware that his role his historically been to be one of the closest allies to the American president.

Both men hailed the special relationship between the United States and the United Kingdom, with each taking time to praise the other for leadership on Ukraine. But Mr. Sunak, who has been in pursuit of a free-trade agreement with the United States — something that Brexit supporters in Britain promised as an alternative to membership in the European Union — will leave Washington with only a modest pact unveiled by both countries on Thursday.

The agreement, called the Atlantic Declaration, will bring the countries closer on research around quantum computing, semiconductor technologies and artificial intelligence, a field in which developments are often faster than the efforts to regulate them.

“What it does is responds to the particular opportunities and challenges that we face right now and into the future,” Mr. Sunak said of the agreement, when asked if it meant that he had failed on his promise to secure a trade deal. Mr. Biden, whose Inflation Reduction Act raised some concerns among allies, said that shoring up manufacturing in the United States and bolstering supply chains would “not hurt any of our allies and friends in terms of the trade pieces.”

Mr. Sunak did not receive an easy victory in his soft campaign to replace NATO’s secretary general, Jens Stoltenberg, who is expected to leave his post in September. Mr. Sunak has publicly pushed for his defense secretary, Ben Wallace, to take the job. When a reporter asked if it was time for a British official to serve as the secretary general, Mr. Sunak grinned widely, but Mr. Biden did not take the bait.

“That remains to be seen,” Mr. Biden said. Earlier in the week, he hosted Prime Minister Mette Frederiksen of Denmark, who is also said to be interested in the job.

Mr. Biden had warm words for Mr. Sunak when it came to the prime minister’s efforts to bring leaders together over issues raised by artificial intelligence. Mr. Sunak is a self-described “techie” who will host a summit on A.I. later this year.

“We are looking to Great Britain to help make that effort to figure out a way through this so we are in full, total cooperation,” Mr. Biden said.

The exchange over A.I. was met with measured skepticism by experts who noted that the efforts of a post-Brexit prime minister may do little to spur leaders to act.

“A London conference on AI regulation is a good thing,” Peter Ricketts, a former national security adviser to Prime Minister David Cameron, wrote on Twitter. “The Brits are good at convening. But this isn’t the same as leading on norm-setting. The heavy lifting is going on in the US-EU dialogue.”

But others pointed out that Mr. Sunak has worked to bring his country closer to an array of allies, including by signing off on a plan with the United States and Australia to develop and deploy nuclear-powered attack submarines.

“Making this whole partnership with the United States and Australia, and even Korea and Singapore, more of a thing is the most natural way he can continue to help Britain punch above its weight,” Michael E. O’Hanlon, a senior fellow at the Brookings Institution, said in an interview.

Mr. Biden and Mr. Sunak have met several times at diplomatic events in recent months, including over coffee when Mr. Biden traveled to Northern Ireland in April. Despite their political differences — Mr. Biden is a moderate liberal and Mr. Sunak a conservative — both men have 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’ relationship with allies around the world after the Trump presidency. And Mr. Sunak, who became prime minister 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. Yet both leaders have low approval ratings, and both lead countries that have so far managed to avoid an economic recession but whose voters feel financially constrained by inflation.

On this visit, Mr. Sunak was under pressure to assure doubters in the United States and at home that, after Brexit, Britain remains as reliable an ally as ever. He came to Washington with gifts, including a custom Barbour jacket, a staple of British outerwear, for Mr. Biden, and both leaders peppered their meetings with historical knowledge about prime minister-presidential relationships past.

“Prime Minister Churchill and Roosevelt met here a little over 70 years ago, and they asserted that the strength of the partnership between Great Britain and the United States was the strength of the free world,” Mr. Biden said. “I still think there’s truth to that assertion.”

There was the occasional personal flourish — mostly from Mr. Sunak — including when the prime minister mentioned at the news conference that their wives had gotten to know each other over spin class dates. At one point, he complimented his lodgings at Blair House, the home across the White House reserved for foreign dignitaries: “The spare room in the flat in Number 10 Downing Street doesn’t quite compare,” he quipped.

Still, their bond did not yet appear to be the same close one that Tony Blair forged with President Bill Clinton and then with President George W. Bush. At another point, Mr. Sunak invoked Churchill’s early-morning wanderings of the White House and “bothering Mrs. Roosevelt.”

“Don’t worry,” Mr. Sunak said, “you won’t see me doing that.”

Stephen Castle contributed reporting from London.