President Biden has an ambitious agenda when he sets off this week on an eight-day trip to the Indo-Pacific.

He’s looking to tighten bonds with longtime allies, make history as the first sitting American president to visit the tiny island state of Papua New Guinea, and spotlight his administration’s commitment to the Pacific. The three-country trip also presents the 80-year-old Mr. Biden, who recently announced he’s running for re-election, with the opportunity to demonstrate that he still has enough in the tank to handle the grueling pace of the presidency.

As he prepares to head west, though, Mr. Biden finds himself in a stalemate with Republican lawmakers over raising America’s debt limit. If the matter is not resolved in the coming weeks, it threatens to spark an economic downturn.

Mr. Biden first heads to Hiroshima, Japan, for the Group of Seven summit. The Japanese prime minister, Fumio Kishida, is this year’s host for the annual gathering of leaders from seven of the world’s biggest economies. He picked his hometown of Hiroshima, where the United States dropped the world’s first atomic bomb in 1945.

The bombing destroyed the city and killed 140,000 people. The United States dropped a second bomb three days later on Nagasaki, killing 70,000 more. Japan surrendered on August 15, 1945, ending World War II and nearly a half-century of aggression in Asia.

The significance of Hiroshima resonates deeply today, given that Russia has made veiled threats of using tactical nuclear weapons in Ukraine, North Korea has stepped up ballistic missile tests, and Iran pushes forward with its nuclear weapons program.

Mr. Biden will then make a brief stopover in Papua New Guinea. He has sought to improve relations with Pacific Island nations amid growing concern at home about China’s military and economic influence in the region.

Finally, Mr. Biden travels to Australia for a summit with his fellow Quad leaders: the Australian prime minister, Anthony Albanese, the Indian prime minister, Narendra Modi, and Mr. Kishida.

The Quad partnership first formed during the response to the 2004 Indian Ocean tsunami that killed some 230,000 people. Since coming to office, Mr. Biden has tried to reinvigorate the Quad as part of his broader effort to put greater focus on the Pacific.

Russia’s invasion of Ukraine and provocative actions by China in the South China Sea and in the Taiwan Strait are expected to be front and center throughout Mr. Biden’s trip.

At last month’s G-7 ministers’ meeting, the alliance pledged a unified front against Chinese threats to Taiwan and Russia’s war. The G-7 includes Britain, Canada, France, Germany, Italy, Japan, and the United States.

Biden administration officials have been troubled by China’s increasing threats against and military maneuvers around Taiwan, the self-governing democracy that Beijing claims as its own. The U.S.-China relationship has also been strained by Speaker Pelosi’s visit to Taipei last August. Those ties were further inflamed after the United States shot down a Chinese spy balloon in February after it traversed the United States.

The G-7 foreign ministers said in their communique that the alliance would look toward “intensifying sanctions” against Russia. How far the G-7 is willing to go remains to be seen.

The looming potential for a debt default by the U.S. government raises a difficult dynamic for Mr. Biden as he heads overseas for the first time since announcing his 2024 campaign.

Since the start of his presidency, Mr. Biden has repeatedly told world leaders that “America is back.” That’s a short-handed way to assure allies that the United States was returning to its historic role as a leader on the international stage following the more inward-looking “America First” foreign policy of President Trump.

But Mr. Biden has also acknowledged that skeptical world leaders have asked him, “For how long?” To that end, top administration officials have said the looming debt limit crisis is a troubling sign.

“It sends a horrible message to nations like Russia and China, who would love nothing more than to be able to point at this and say, ‘See the United States is not a reliable partner. The United States is not a stable leader of peace and security around the world,’” the White House National Security Council spokesman, John Kirby, said.

The Congressional Budget Office said on Friday that there was a “significant risk” that the federal government could run out of cash sometime in the first two weeks of June unless Congress agrees to raise the $31.4 trillion borrowing cap.

With the brief stop in Papua New Guinea to meet with Pacific Island leaders, Mr. Biden gets the chance to show the United States is serious about remaining engaged for the long term in the Pacific Islands.

The area has received diminished attention from the United State in the aftermath of the Cold War and China has increasingly filled the vacuum — through increased aid, development and security cooperation. Mr. Biden has said that he’s committed to changing that dynamic.

Last September, Mr. Biden hosted leaders from more than a dozen Pacific Island countries at the White House, announcing a new strategy to help to assist the region on climate change and maritime security. His administration also recently opened embassies in the Solomon Islands and Tonga, and has plans to open one in Kiribati.

He’ll be the first sitting president to visit the island nation of about 9 million people. The Chinese president, Xi Jinping, made a visit to Papua New Guinea in 2018.

Mr. Biden is going to be spending plenty of time with the Indian prime minister in the coming weeks. Mr. Modi is among eight leaders of non-G-7 countries who were invited by Mr. Kishida to join the meeting of major industrial nations at Hiroshima. He’ll also join Mr. Biden’s meeting with Pacific Island leaders in Papua New Guinea.

Then Messrs. Biden, Modi, and Kishida will all make their way to Australia for a meeting of the Quad to be hosted by Mr. Albanese at Sydney. Mr. Biden won’t have to wait long to see Mr. Modi again: The president is hosting him for a state visit on June 22.