US President Barack Obama on Monday urged South Sudan to show restraint after heavy border fighting with Sudan as officials voiced alarm over growing hunger, refugees and fears of all-out war.

As officials from Sudan and South Sudan held crisis talks in Ethiopia, Obama spoke by telephone to US-backed South Sudan's President Salva Kiir to voice concern over bloodshed at the border and within Sudan's Southern Kordofan state.

"President Obama underscored the importance of avoiding unilateral actions, and asked President Kiir to ensure that South Sudan's military exercises maximum restraint and is not involved in or supporting fighting along the border, particularly in Southern Kordofan," a White House statement said.