All 15 members approved a statement calling for de-escalation, the "restoration of calm" and a resumption of peace talks.
At least 133 Palestinians have been killed since Israel began its operation five days ago, Palestinian sources say.
Israel says it has been hit by over 40 rockets since Friday, suffering damage.
It is the first time since Israel's offensive began that the UN Security Council has issued a statement, with members previously divided on their response.
Text of UN Security Council statement
The Security Council members expressed serious concern regarding the crisis related to Gaza and the protection and welfare of civilians on both sides.
The Security Council members further called for respect for international humanitarian law, including the protection of civilians.
The Security Council members also expressed their support for the resumption of direct negotiations between the Israelis and Palestinians with the aim of achieving a comprehensive peace agreement based on the two-state solution.
In the latest violence
- Two nephews of Hamas ex-PM Ismail Haniyeh were among a group of six men killed in the Sheikh Radwan district of Gaza City, Palestinian medics said
- A large fire broke out in a UN humanitarian relief compound in the east of Gaza City. Israel said it was caused by Hamas rockets falling short, though this has not been confirmed
- Israel hit a residential home for disabled people in Beit Lahiya, Palestinian officials said. Two female residents were killed and four other people seriously injured, they said. Israel did not comment
- Six Palestinians were killed in three separate attacks in northern and central Gaza, the Palestinian health ministry said
- At least one mosque in the central Gaza Strip was bombed, according to Hamas, which said it was the first attack of its kind since Israel began its offensive. Israel's military said the building had been used to store weapons
- Israeli forces said they had destroyed several missiles launched by militants in flight. Hamas said it had fired four rockets at the Israeli city of Ashdod