The cease-fire would allow for the delivery of "urgently needed assistance," the Security Council said.
The 15-nation council also proclaimed its support for "a comprehensive peace based on the vision of a region where two democratic states, Israel and Palestine, live side by side in peace with secure and recognized borders as envisioned in Security Council resolution 1850 (2008)."
The call for a cease-fire came after Hamas and Israel began firing again at each other Sunday after a temporary cease-fire failed.
A temporary truce in the conflict Saturday had enabled medical supplies to be brought into Gaza, families to emerge from shelters and people to dig out the dead from piles of rubble.
But Sunday, Israel said that because of "incessant rocket fire" out of Gaza, it had restarted its Operation Protective Edge, even as Hamas said it agreed to a 24-hour U.N.-mediated cease-fire.
Israeli Prime Minister Benjamin Netanyahu dismissed the call by Hamas for a cease-fire, saying the group violated its own call for a brief stoppage in violence.
"We hope we can get a sustainable quiet as soon as possible. I think the only path to do that is by adopting the Egyptian initiative" and by addressing two underlying issues, he told CNN's "State of the Union with Candy Crowley."
He said those issues are peace for Israel through demilitarizing Gaza, and social and economic relief for the residents of Gaza.
Hamas, the militant group that is in control of the besieged Palestinian territory, began firing rockets again Sunday afternoon, blaming a "lack of commitment" from Israel.
The Israeli Security Cabinet had agreed to a U.N. request late Saturday to extend a cease-fire that started Saturday morning until midnight Sunday (5 p.m. ET Sunday), on the condition that its military could keep dismantling and destroying Hamas' tunnels, according to senior Israeli officials.
Israel said it resumed its offensive because it was still being attacked.
"Following Hamas' incessant rocket fire throughout the humanitarian window, which was agreed upon for the welfare of the civilian population in Gaza, the IDF will now resume its aerial, naval and ground activity in the Gaza Strip," the IDF said.
A poll of 504 Hebrew-speaking Israelis suggests that an overwhelming majority want the offensive to continue, the Jerusalem Post reported Sunday.
It said the poll, sponsored by a political strategist who used to work with Netanyahu, indicated 86.5% responded that Israel shouldn't accept a cease-fire.
Official: Palestinian leaders headed to talks
Palestinian Authority President Mahmoud Abbas is forming a delegation that would head to the Egyptian capital, Cairo, to engage in more diplomacy in the Mideast conflict, said Mohammad Shtayyeh, a senior adviser to Abbas.
Abbas is waiting for a final answer on the initiative from Hamas leaders, who were meeting in Qatar, he said.
Israel has a "hidden agenda," Shtayyeh said.
"Israel wanted to keep Gaza separate from the rest of the Palestinian territory," he said.
He said Israeli troops occupy 50% of Gaza and should withdraw. Not doing so endangers chances for a cease-fire, he said.