Eswatini activists have urged the High Court to declare as unconstitutional the country's acceptance of five foreign nationals deported from the United States where they had been jailed for crimes including murder.

The men from Vietnam, Laos, Yemen, Cuba and Jamaica were flown to the Southern African country by US military aeroplane in July as part of Washington's programme of deporting migrants to third countries.

In an urgent court application to the Eswatini High Court, three legal and civil society groups said that the deal was unconstitutional because its terms had not been made known and there had been no consultation with the public or parliament.

They called on the government of Eswatini to release the full terms of its agreement with the United States.

Claim of 'executive overreach'

"The circumstances under which this agreement has been concluded raise serious concerns about executive overreach, human rights and national security," they said in a statement announcing the court action.

The five deportees are being held in solitary confinement in a maximum security prison that is already at 171% capacity, the statement said.

Last week, the neighbouring South Africa protested to Eswatini about its acceptance of the convicted criminals, saying that it was concerned about their profiles and potential "adverse impact" on its own security.