South Sudan's First Vice President Riek Machar has accused Uganda of violating a United Nations arms embargo by entering the country with armoured and air force units, and conducting airstrikes around the country.

In a letter addressed to the UN, African Union and the IGAD regional bloc, Machar said Uganda's military intervention in South Sudan had violated a 2018 peace deal, which ended a brutal five-year civil war.

Uganda said it had deployed troops in South Sudan earlier this month at the request of the government there, following a breakdown in the turbulent relationship between Machar and President Salva Kiir.

In early March security forces rounded up several of Machar's most senior allies, following clashes in the country's northeast between the military and the White Army ethnic militia, which the government accuses Machar of supporting.

Though they fought together against Kiir's forces during the 2013-2018 conflict, Machar's SPLM-IO party denies any ongoing links with the White Army.

The UN has warned a rise in hate speech could plunge the country back to war along ethnic lines.

Uganda fears a full-blown conflagration in its oil-producing northern neighbour could send waves of refugees across the border and potentially create instability.

"The Ugandan forces are currently taking part in airstrikes against civilians," Machar said in the March 23 letter, urging pressure on Uganda to withdraw its troops.

A spokesperson for Machar's office verified the authenticity of the letter seen by Reuters.

Uganda and South Sudan's military spokesmen did not immediately respond to requests for comment about the potential violation of the embargo, which has been in place since July 2018.

South Sudan's army attacked SPLM-IO forces stationed at a camp near the capital Juba on Monday night, the party's military spokesperson Lam Paul Gabriel said on X. South Sudan's information minister did not immediately respond to the accusation.

Last week Uganda's parliament retrospectively approved the deployment in South Sudan, first announced on March 11.

Ugandan defence minister Jacob Markson Oboth said the deployment was "to avoid a security catastrophe" in Africa's newest nation.

In a series of since-deleted posts published on X in the early hours of Sunday, Uganda's military chief Muhoozi Kainerugaba said: "I'm tired of killing Nuer," referring to Machar's ethnic group.

"Tell your leader Riek Machar to come and kneel down before 'our' President H.E Salva Kiir," wrote Kainerugaba, who has a history of making inflammatory statements that have previously sparked diplomatic tensions in the region.