Nickolay Mladenov delivered the stark warning as the council remained deadlocked over how to respond to the flare-up between Palestinian militants in the Gaza Strip and Israel.
“This latest round of attacks is a warning to all of how close to the brink of war we are every day,” said Mladenov, who spoke via video link from Jerusalem.
But Kuwait, a non-permanent council member that represents Arab countries, blocked the US-drafted statement, arguing that it had presented its own draft resolution that addressed the crisis.
The exchange of fire on Tuesday and into the early hours of Wednesday began with a barrage of rocket and mortars into Israel from Gaza, prompting Israel to respond with strikes on 65 militant sites in the Gaza Strip.
The violence was the most serious escalation since the 2014 war between Israel and Hamas and followed weeks of Palestinian protests in which more than 100 Palestinians have been shot and killed by Israeli forces.
“No one in Gaza can afford another war,” said Mladenov.
Kuwait is pushing for a vote at the council this week on its draft resolution calling for “the consideration of measures” for the protection of Palestinian civilians, according to the text obtained by AFP.
The United States, which has veto power in the council, will oppose the measure, Israeli Ambassador Danny Danon told reporters.
“This increasingly heavy silence, which is becoming deafening, is not acceptable,” said French Ambassador Francois Delattre.
“It is not acceptable for the Palestinian and Israeli populations, who are affected by this conflict. It is not acceptable for the world that is watching us,” he said.