SYDNEY, Australia — The first group of refugees from Australia’s offshore detention centers is expected to leave for the United States “in the coming weeks,” Australia’s prime minister announced Wednesday.

In a video shared on social media, Prime Minister Malcolm Turnbull thanked President Trump for honoring a deal reached by the Obama administration, which Mr. Trump had criticized, in which the United States agreed to accept hundreds of refugees from the centers, one on Manus Island in Papua New Guinea and one on Nauru, an island nation to the east.

“Around 50 refugees from P.N.G. and Nauru will be accepted in this first group, and they’ll be notified in coming days,” Mr. Turnbull said on Wednesday. “Vetting and processing by the United States will continue, and further decisions by U.S. authorities in respect of others are expected in due course.”

An official with the State Department confirmed that 54 approved refugees would be notified in the coming days and travel to the United States in the coming weeks. Little is known about the group, but the official said that the refugees were similar in makeup to other groups that country admits for resettlement.