A Jamaican man deported from the US to Eswatini under President Donald Trump's tough new immigration rules has been sent on to Jamaica, the Eswatini government has said.

Orville Isaac Etoria, 62, was voluntarily repatriated at the weekend and was warmly welcomed by members of his family, it added.

However, his treatment has been condemned by the Legal Aid Society of New York, which says Etoria came to the US as a child and had lawful permanent resident status there for decades.

Etoria and four other individuals - from Cuba, Laos, Vietnam, and Yemen - were described by the US government as depraved monsters when they were expelled to Eswatini in July.

Since then, they have been held in solitary confinement in a maximum security prison in the capital city Mbabane.

Lawyers for the remaining four deportees say they have been unable to contact them. However, Eswatini's government has stated that it is making efforts to repatriate them all.

Trump's pledge to conduct mass deportations was a centerpiece of his election campaign, gaining widespread support.

In some cases, individuals are expelled to countries where they lack any connections.

Etoria had transformed his life while serving a 25-year sentence for murder and reintegrated into American society before he was deported and imprisoned again in Eswatini without due process, according to the Legal Aid Society.

Activists in Eswatini have also denounced the deal as unconstitutional and held protests outside the American embassy.

Rights groups have initiated legal proceedings in a bid to overturn it, arguing that the government could not establish such an agreement without parliamentary approval.

Eswatini's government is asserting its actions were within its legal powers.

Eswatini is the last absolute monarchy in Africa, previously known as Swaziland, a small, landlocked country bordered by South Africa and Mozambique, ruled by King Mswati III since 1986.