The resolution received five votes in favor, four votes against and six abstentions. Those who voted it down were the US, the UK, France and Japan.
While the Palestinian group Hamas was not specifically mentioned in Russia's draft resolution, all civilian deaths were condemned.
Russia's UN ambassador, Vassily Nebenzia, said today's vote showed who are in favor of a truce or halt to indiscriminate bombings and the provision of humanitarian assistance.
"The entire world waited with bated breath for the Security Council to take steps in order to put an end to the bloodletting. But the delegations of the Western countries have basically stomped on those expectations," said Nebenzia.
US Ambassador to the UN Linda Thomas-Greenfield said Russia's resolution was put forward without any consultations and made no mention of Hamas.
For his part, Palestine's ambassador to the UN Riyad Mansour accused the UN Security Council of watching the attacks against 2 million people in the Gaza Strip for 10 days.
Stressing that people in Gaza are being killed, injured, displaced and terrorized, Mansour said Israel has not spared a single Palestinian family in Gaza.
"No one should forget that these are human lives, that Palestinian lives matter too. And no one should entertain the illusion that killing more Palestinians will ever make Israelis more secure," he added.
Another resolution, which was drafted by Brazil, is set to be voted on Tuesday.