SAN JOSE, Costa Rica — Secretary of State Antony Blinken said Tuesday that the United States would soon distribute millions of doses of coronavirus vaccines around the world, including in Latin America, which is struggling to obtain them for its citizens amid rising hospitalization rates.

But the question on the minds of many — which countries will receive doses first and how quickly will they be delivered — remained unanswered as Blinken began his first official visit to the region.

“Sometime in the next week to two weeks we will be announcing the process by which we will distribute those vaccines,” Blinken said at a news conference in San Jose with Costa Rican President Carlos Alvarado Quesada.

President Biden promised to provide 80 million doses to other countries by the end of June. But his administration has not provided further details amid a global competition for vaccines that has left many developing countries far behind the industrialized West.

In Costa Rica, a country of 5 million people that recently imposed nationwide driving restrictions to lessen the strain on hospitals overloaded with covid-19 patients, the question loomed large. Both Blinken and Alvarado Quesada were asked whether Costa Rica would receive doses this summer.

Alvarado Quesada made clear after his meeting with Blinken and top aides that no firm promises had been made yet.

“We look forward to what the United States is going to announce in the matter of vaccines,” he told reporters at San Jose’s presidential palace. “We hope to be part of the countries that receive that.”

In Washington, the distribution of vaccines to Latin America by China and Russia has been viewed as part of a geostrategic competition.

Beijing has shipped more than 165 million doses of its vaccine to Latin America and the Caribbean. Some Latin American countries rely heavily on the Chinese-made vaccines, including El Salvador, Brazil, Chile and Uruguay.

The United States has focused on vaccinating its own population, distributing only 4 million doses of the AstraZeneca vaccine to Canada and Mexico while committing $4 billion to Covax, the international platform supported by the World Health Organization that donates vaccines to countries in need.

The coronavirus initially damaged China’s public image after it became the global epicenter of the outbreak, but its lightning-fast distribution of its vaccines has shifted the conversation despite some questions about the efficacy of its jabs.

China denies it distributes the vaccine in exchange for political favors. Blinken said the United States would not attach strings to its vaccine donations.

“We will focus on equity,” he said. “We’ll focus on science. We’ll work in coordination with Covax and we will distribute vaccines without political requirements of those receiving them.”