The 15-member body will meet at 10 am local time (5 pm Jerusalem time) on Thursday to discuss the violence that is building up to the most serious hostilities between Israel and Hamas militants in Gaza since an eight-day war in 2012.
Rwanda, which is president of the council for July, said there would be a public briefing by Ban and the Israeli and Palestinian UN ambassadors before closed-door consultations.
Ban spoke on escalating tensions with Gaza in an interview to the BBC saying that the situation "is on a knife-edge" and warning that the Middle East "cannot afford another full-blown war."
"The deteriorating situation is leading to a downward spiral which could quickly get out of control," said Ban. "The risk of violence expanding further still is real."
Israeli air strikes shook Gaza every few minutes on Wednesday, and terrorists kept up rocket fire at Israel's heartland in intensifying warfare that Palestinian officials said has killed at least 47 people.
"Gaza is on a knife edge," Ban told reporters on Wednesday. "I firmly condemn the multiple rocket attacks launched from Gaza on Israel. Such attacks are unacceptable and must stop."
"I also urged (Israeli) Prime Minister (Benjamin) Netanyahu to exercise maximum restraint and to respect international obligations to protect civilians. I condemn the rising number of civilian lives lost in Gaza," he said.
Ban spent the day speaking with regional and world leaders, including Netanyahu, Palestinian President Mahmoud Abbas, US Secretary of State John Kerry, Egyptian President Abdel Fattah al-Sisi, the king of Saudi Arabia and the emir of Qatar.
"Regional leaders have a vital role to play and I urged President Sisi and others to help facilitate a return to the November 2012 ceasefire agreement," Ban said. "The risk of violence expanding further still is real. Gaza, and the region as a whole, cannot afford another full-blown war."
Cairo brokered a truce in the conflict two years ago, but the current military government's hostility toward Islamists in general and to Hamas, which it accuses of aiding fellow militants in Egypt's Sinai Peninsula, could make a mediation role more difficult. Hamas denies those allegations.
Ban said Sisi assured him he would continue to use his leadership to urge maximum restraint by both sides.