Mr Kiir is scheduled to sign a deal to end months of brutal civil war later on Wednesday, although his spokesman said he still had "reservations".
Rebel leader Riek Machar signed it last week but Mr Kiir refused.
Fighting between forces loyal to the two men has displaced over 2.2 million people.
In a Security Council briefing, the UN's humanitarian chief Stephen O'Brien warned conditions were deteriorating, saying he heard multiple accounts of atrocities, including people being burned in their homes.
"The scope and level of cruelty that has characterised the attacks against civilians suggests a depth of antipathy that goes beyond political differences," he said.
Afterwards, the current president of the Security Council, Nigerian Ambassador Joy Ogwu, said the council was united over South Sudan.
"We all agree on measures to be taken that anybody who is found culpable will be held accountable," she said.
A US-drafted resolution would impose an arms embargo and targeted sanctions, unless Mr Kiir signs.
The two sides have disputed the detail of the peace proposal, which would see Mr Machar return as vice-president.
South Sudan is the world's youngest country, becoming independent in 2011.
Several ceasefires have been agreed and broken since conflict broke out in 2013, after the president accused Mr Machar of attempting a coup.
The UN has said it is ready to "act immediately" unless South Sudan's President Salva Kiir signs a peace deal with rebels.