The fighting started when Kiir accused Machar of attempting a coup in the oil-rich but impoverished nation.
Machar denied this, in turn accusing the president of conducting a violent purge of opponents. He has so far refused to hold direct talks with Kiir.
Fighting has spread across the country, with the rebels seizing several areas in the oil-rich north.
Aid workers have stepped up warnings of a worsening crisis for civilians affected by the conflict in the landlocked country of almost 11 million people.
Britain’s Hague said he had also discussed with Museveni the issue of access for humanitarian aid in the parts of South Sudan affected by the fighting.
The violence has forced around 200,000 people to flee their homes and “affected many hundreds of thousands of people indirectly”, the UN’s Lanzer said.
About 57,000 are seeking refuge with badly overstretched UN peacekeepers.
The UN peacekeeping force said this week that atrocities are continuing to occur across the country, which won independence from Sudan in 2011 after decades of civil war.
One of the hardest hit areas is Bor, the capital of Jonglei state and situated just 200 kilometres (125 miles) north of Juba.
Tens of thousands have fled, many paddling in simple boats across the crocodile-infested White Nile river to escape the fighting.
The conflict has been marked by an upsurge of ethnic violence pitting members of Kiir’s Dinka tribe against Machar’s Nuer community, and the army has set up committees to probe the killing of “innocent people”.
The United Nations has reported extra-judicial killings of civilians and captured soldiers and the discovery of large numbers of bodies in Juba as well as in the towns of Bor and Malakal.
Machar told AFP this week he was not yet ready to agree to an immediate ceasefire nor hold face-to-face talks with Kiir.
Kiir has described the war as “senseless” but has ruled out power-sharing with the rebels.