The 10 were on a mission to provide humanitarian aid to the residents of Yei.
The workers' wellbeing remains unknown, the statement added.
Of the 10 who were kidnapped, one was from the U.N. Office for the Coordination of Humanitarian Affairs, two from the U.N. International Children's Fund, one from the South Sudanese Development Organization, two from South Sudanese NGO Across, three from Plan International and one from Action Africa Help.
The president, while addressing mourners of the late army chief, General James Ajongo Mawut in the capital, Juba Tuesday accused opposition groups of working to ensure he relinquishes power.
The Humanitarian Coordinator for South Sudan, Alain Noudehou demanded their swift return.
"The trend toward targeting humanitarian work is on a daily basis increasing", said Mr. Yakani, whose 60 staff members around the country report daily on the conditions.
I neither deny nor accept who are the responsible of this, we are investigating because it is our territory, but we must not dismiss the presence of other armed forces, Paul Gabriel remarked.
Conflict that erupted in December 2013 has claimed tens of thousands of lives, caused Africa's largest refugee crisis and left parts of South Sudan on the brink of starvation.
Aid workers are often targeted by armed groups operating in South Sudan, which has been in the grip of war between supporters of President Salva Kiir and those of his former deputy Riek Machar since 2013.
The war - described by Filippo Grandi, the United Nations high commissioner for refugees, as having a human cost of "epic proportions" - has created Africa's biggest refugee crisis since the 1994 Rwandan genocide.