The council held protracted talks on the wording of the first statement on the conflict which came several hours after the ceasefire was declared.
"The members of the council called on the parties to uphold the agreement and to act seriously to implement its provisions in good faith," said the statement.
The international community also had to help improve living conditions in Gaza by "providing additional emergency aid through appropriate established channels," the council said.
There had to be "expeditious and unimpeded delivery of such humanitarian assistance, including of food, fuel and medical treatment," said the statement.
The council and UN secretary general Ban Ki-moon both praised the role of Egypt's President President Mohamed Morsi in setting up the ceasefire.
"I commend the parties for stepping back from the brink, and I commend President Morsi of Egypt for his exceptional leadership," Ban said in a briefing to the council by videolink from Israel where he has been taking part in talks.
The Security Council members "strongly commend" Morsi for his efforts to end the violence, their statement said.