Echoing a call made earlier today by South Sudanese religious leaders, ambassadors from the council's 15 member states met with senior government ministers in Juba and all spoke in favour of sending an additional 4,000 troops to the 13,000-strong mission, known as UNMISS.
One of the ambassadors, who asked not to be named, told AFP he thought the South Sudanese ministers "were surprised to see that the Security Council spoke with one voice.
The two died when artillery fire hit a UN base during July clashes between forces loyal to President Salva Kiir and those of rebel leader Riek Machar.
The upsurge threatened a fragile peace accord signed last year to end a devastating 18-month civil war which left tens of thousands dead.
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China and Russia abstained from an August 12 Security Council vote on the resolution that authorised deploying a protection force with a more robust mandate than that of UNMISS.
UNMISS faced considerable criticism over its failure to protect civilians during the July fighting.
Those at today's meeting emerged on a conciliatory note.
"I want to assure the people of South Sudan that the rumour that the UN has come to impose on us and bring in foreign forces to take the freedom of our country is not there," said Government Affairs Minister Martin Elia Lomoro.
Lomoro said the "modalities" of deploying the new force were being discussed but he did not state that his government had dropped its opposition.
US Ambassador Samantha Power said the meeting was "useful" because "we got to debunk, as the Security Council, some of the myths that have existed about what the Security Council has intended.
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