During the Friday meeting, the UN High Commissioner for Human Rights, Navi Pillay called for an International Criminal Court investigation into the conflict and presented a grim assessment of the situation in Syria.
"I have urged the Security Council to refer the situation to the International Criminal Court for investigation of war crimes and crimes against humanity on the part of all parties engaged in this conflict," Pillay told reporters after the UNSC meeting.
The UN Under-Secretary-General for Humanitarian Affairs, Valerie Amos also called for greater access within Syria and an increase in funds for addressing the humanitarian needs in the Arab country.
Amos went on to say that around four million Syrians are in need of assistance and two million more have been displaced due to the ongoing conflict in the country.
"We have thousands of people who are living out in the open under tattered tents, no access to food, no access to medical equipment or to medical help," she said. "We urgently need funds and we urgently need to increase our capacity."
She said that the UN urgently needs funding for its USD-1.5-billion humanitarian appeal.
The Security Council members, however, are still skeptical about a possible agreement.
Syria has been experiencing unrest since March 2011. Many people, including large numbers of Army and security personnel, have been killed in the violence.
According to a UN report, militants from 29 countries have so far infiltrated into Syria to fight against the Damascus government, most of whom are extremist Salafists.
The Syrian government has said that the chaos is being orchestrated from outside the country, and that a very large number of the militants operating in the country are foreign nationals.