A Jamaican man deported from the United States to the southern African country of Eswatini two months ago has been repatriated to Jamaica, Eswatini's government said.

The man, named in the government statement as Orville Isaac Etoria, was one of five third-country nationals deported to Eswatini in July by the Trump administration as part of its crackdown on illegal immigration.

The other four - from Cuba, Laos, Vietnam and Yemen - are still being held in detention there while efforts to repatriate them are ongoing, Eswatini's government said.

"Mr Etoria has safely returned to Jamaica, where he was warmly welcomed by members of his family," said the Eswatini government statement issued on Monday.

He was repatriated on Sunday of his own volition, it said.

President Donald Trump aims to deport millions of immigrants in the U.S. illegally and his administration has sought to ramp up removals to third countries, including South Sudan and Ghana.

The U.S. Department of Homeland Security said in July that the five individuals sent to Eswatini, who were all convicted criminals, were "so uniquely barbaric that their own countries won't take them back." Etoria had been convicted of murder, it said.

But Eswatini's government said shortly after that some of the countries had reached out to say it was not true that they had rejected their citizens.

Critics say the U.S. removals to third countries aim to stoke fear among migrants and encourage them to "self deport" to their home countries rather than be sent to distant places they have no connection with.

Etoria, who arrived in the U.S. as a child, had already served a 25-year sentence for his crime and been released when he was deported and imprisoned again in Eswatini without due process, according to the New York-based Legal Aid Society.