The talks have faced delays after Kiir refused a rebel demand to release 11 high-level political detainees.
Death toll 'substantially' higher
At the UN, Ladsous said he estimated that the death toll was "very substantially in excess" of the 1,000 deaths the UN cited just after the conflict erupted on December 15.
The violence began as a clash between rival army units in what President Kiir said was an attempted coup by Machar.
Machar denied that accusation, accusing Kiir of trying to root out political opponents.
The conflict has trimmed South Sudan's oil production by around a fifth, depriving the impoverished nation of its main source of foreign currency.
- AFP, Reuters, AP