A trip by Vice President Kamala Harris to Southeast Asia will give the Biden administration an opportunity to put the focus back on countering China at a time when the U.S.’s chaotic exit from Afghanistan is raising questions about Washington’s reliability as an ally.

Ms. Harris departs on Friday for Singapore and Vietnam, visits that will be the culmination of months of diplomatic outreach to the region, underscoring a shift in priorities away from the war on terror and toward containment of competing powers.

During her trip, Ms. Harris is expected to focus on global health, economic partnerships and security in the region, according to senior administration officials. She will deliver a speech in Singapore detailing her vision for the Indo-Pacific and launch a Southeast Asia regional office for the U.S. Centers for Disease Control and Prevention in Vietnam.

Ms. Harris will also meet with government officials and business leaders to speak about supply-chain issues. The Biden administration has been working to address a global semiconductor shortage, which has caused production slowdowns from appliances to computers and cars.

A surge in Covid-19 cases in the largely unvaccinated region has also led to lockdowns in countries including Vietnam, Thailand and Malaysia—major exporters of electronics and other goods—that forced factory closures and further disrupted global supply chains. U.S. business representatives have pressed the Biden administration to accelerate aid to the region.

More broadly, support from governments in the region is critical to the U.S.’s long-term interests in the Indo-Pacific region, where Beijing has aggressively sought greater influence over poorer neighbors and expanded its claims in the South China Sea.

“Southeast Asia is one of the major arenas of U.S.-China strategic competition,” said Renato Cruz De Castro, a professor of international studies at De La Salle University in Manila. “There’s a perception in Washington that China has been earning a lot of points lately, so there is a sense of urgency.”

Ms. Harris is tasked with repairing relationships that eroded under former President Donald Trump, analysts say. During his term, several ambassador posts were left empty for long periods and attendance at regional forums was greatly reduced, which was widely perceived as a snub.

As America ends its war in Afghanistan after 20 years, a WSJ analysis of data shows how the Taliban gradually took back control of the country and expanded its military presence after being toppled in 2001. Photo Illustration: George Downs The Wall Street Journal Interactive Edition

But Southeast Asia’s gradual drift away from Washington goes back further, to ex-President Barack Obama’s unfinished “Asia rebalance” policy. Key agreements reached during his presidency stalled early on, including a major trade agreement with Pacific nations and an enhanced defense pact with the Philippines.

Even as ties improve, there will be limits, analysts say. The challenge for Ms. Harris will be not only to convince her Southeast Asian counterparts that Washington is a reliable partner, but that they are seen as more than pawns in a great power struggle. Regional leaders including Singapore Prime Minister Lee Hsien Loong have long voiced resistance to choosing sides.

Aaron Connelly, a Singapore-based researcher with the International Institute for Strategic Studies, a London-based think tank, said smaller countries confronted with a rising power typically have three options: They align with it, hedge, or balance against it by siding with its adversary.

“Most countries in Southeast Asia are hedging,” Mr. Connelly said. “In the short-term, none of these countries are going to get off the fence and side with the U.S., but they can be persuaded to make choices on discrete issues in ways that favor the U.S.”

The rushed evacuations in Afghanistan, which have drawn parallels to the American exit from Saigon in the final days of the Vietnam War, will also loom large over Ms. Harris’s trip.

Asked if the situation in Afghanistan posed a problem for Ms. Harris in gaining the trust of officials in Southeast Asia, a senior administration official said the White House’s current engagement in the two regions was too different to compare.

Ms. Harris will build on the momentum of earlier visits by other senior U.S. officials, pledging increased cooperation on healthcare, economic recovery and regional security. Since early June, Southeast Asia has been visited by Deputy Secretary of State Wendy Sherman, Defense Secretary Lloyd Austin and U.S. Ambassador to the United Nations Linda Thomas-Greenfield. Secretary of State Antony Blinken met virtually with Southeast Asian ministers in early August.

Recent engagements have largely focused on Covid-19 assistance, as much of Southeast Asia has struggled to obtain vaccine supplies and several countries are facing devastating surges driven by the Delta variant. In early August, the White House said it had shipped more than 23 million doses to the region and provided $158 million in health and humanitarian aid.

Countering China’s expansion in the South China Sea remains one of the U.S.’s top priorities. Over the past five years, Beijing has built up a massive presence by militarizing artificial islands and using civilian fleets, widely regarded as maritime militias, to occupy new areas and advance its claims. Analysts say a more comprehensive U.S. military presence in the region could ward off further encroachment and prevent an escalation that neither side wants.

“It’s deterrence by denial, that’s really what it’s all about: Making sure that China doesn’t ever believe they’re going to go unnoticed or be able to exploit disputed territory without a response,” said James Siebens, a fellow with the Defense Strategy and Planning program at the U.S.-based Stimson Center.

Vietnam, which claims parts of the South China Sea, has emerged as an attractive partner to head off further Chinese expansion, as Washington’s relationship with the Philippines, a treaty ally, has been strained in recent years. When Ms. Harris meets with Vietnamese leaders, she is expected to push for an upgrade in relations from a “comprehensive” to a “strategic” partnership, which could streamline high-level diplomatic access and defense cooperation, analysts say. Senior administration officials declined to comment on whether an upgrade was in the works.

The U.S. has a similar arrangement with Singapore, which grants it access to air and naval bases and enables the sharing of defense technology.

Ties between the U.S. and Philippines have gotten more volatile under President Rodrigo Duterte, whose single term ends next year. The Philippine leader has threatened to sever ties with the U.S., partly over criticisms of his administration’s alleged involvement in human rights abuses including extrajudicial killings linked to his war on drugs. Rights groups say more than 12,000 people were killed in antidrug operations since he took office.

Human rights is also a potential complication to improving ties with Vietnam. President Biden has pledged to give priority to human rights in his administration’s foreign policy.

Vietnam’s communist leadership has been criticized for its human rights record. When Mr. Obama visited the country in 2016, several activists were detained in a wave of arrests before his arrival, human rights groups say. Vietnamese activists and bloggers are often subject to harassment and more than 130 political prisoners are behind bars, according to Human Rights Watch.

Ms. Harris’s travel to Singapore and Vietnam will mark her second foreign trip as vice president. She traveled to Mexico and Guatemala in June, where she received bipartisan criticism for some missteps.

Ms. Harris was criticized for missteps during her first trip abroad, to Mexico and Guatemala; she is pictured leaving Mexico in June.

Photo: Eyepix/Zuma Press

Write to Feliz Solomon at feliz.solomon@wsj.com and Tarini Parti at Tarini.Parti@wsj.com