The appeal was made in a presidential statement adopted by the UN Security council at an emergency meeting, which began at 12.04 a.m., Xinhua reported.
"The Security Council urged all parties to accept and implement the humanitarian ceasefire into the upcoming Eid festivities and beyond," the statement said.
"The Security Council expresses grave concern regarding the deterioration in the situation as a result of the crisis related to Gaza and the loss of civilians and casualties," the statement said.
The urgent council meeting came after the collapse of a UN-proposed humanitarian truce in Gaza.
A Palestinian was killed and 10 others were injured Sunday after Israeli war jets resumed air strikes on Gaza, where a previous UN-proposed humanitarian ceasefire between Israel and Hamas had collapsed.
On Sunday, Hamas spokesman Sami Abu Zuhri said that Hamas and the Palestinian factions agreed to accept the UN-proposed ceasefire for 24 hours, but Israel rejected it.
Efforts to reach a ceasefire between Israel and Hamas have so far failed.
"The Security Council emphasises that civilian and humanitarian facilities, including those of the UN, must be respected and protected," the statement said.
At least 15 people were reportedly killed in Thursday's attack on a school in Beit Hanoun, which was run by the UN Relief and Works Agency for Palestine Refugees (UNRWA).
So far, 18 medical facilities, including five UNRWA health clinics, have been hit by air strikes and shelling.
The Security Council "stressed the need for immediate provision of humanitarian assistance to the Palestinian civilian population in the Gaza Strip, including through urgent additional contribution to UNRWA," it said.
More than 100,000 Gazans, or five percent of the total population, have sought refuge in UNRWA facilities since the conflict began.
Israel launched a large-scale operation on Gaza July 8 dubbed Operation Protective Edge.
A total of 1,030 Palestinians and 43 Israelis have been killed and more than 6,000 Palestinians injured.