The 15-member council also demanded that fighters from the Islamic State group and the Al-Qaeda-linked Al-Nusra Front withdraw, and that bombing raids on the Palestinian refugee camp be halted.
Fighting has intensified since April 1 when IS fighters seized part of the camp, clashing with other armed groups as Syrian government forces besieged the area.
The council on Monday met for the second time in two weeks to discuss the Yarmuk crisis after Secretary General Ban Ki-moon said action must be taken to prevent a "massacre" at the camp.
In a unanimous statement, the council "called for unhindered humanitarian access to the Yarmuk camp and for the protection of civilians inside the camp."
The council heard a report from Pierre Krahenbuhl, head of the Palestinian UNRWA relief agency, who returned from a recent visit to the area to try to secure access to Yarmuk.
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The UN official later told reporters that the situation in Yarmuk "remains very extreme in both circumstances and hardship" but he declined to comment on military operations by the various armed groups.
Palestinian officials said last week that IS fighters had retreated.
Krahenbuhl noted that a $30 million appeal for funding for the Yarmuk aid effort had received few pledges.
The UN official proposed that a delegation from the Security Council travel to Yarmuk for a first-hand view of the situation.
Once home to around 160,000 Palestinian residents as well as a number of Syrians, Yarmuk's population had shrunk to just 18,000 by the time IS entered the camp.
According to Palestinian sources, some 2,500 civilians have managed to escape the camp, located just seven kilometers (four miles) from Damascus.