Over the past weeks, Israelis have been targeted in attacks where they've been "run over, stabbed, or even hacked to death," said Israeli Prime Minister Benjamin Netanyahu, who spoke alongside Ban at a news conference.
Palestinians report, meanwhile, that 45 Palestinians have been killed by Israeli security forces in the West Bank, Jerusalem and Gaza.
Ban has stature as the top official in the United Nations, but that hardly guarantees he'll be able to soothe tensions that have been simmering not just for weeks, but for decades.
His balancing act was apparent during the joint news conference, where Netanyahu accused Palestinian Authority President Mahmoud Abbas of stoking fears that Israel threatens the holy site at al-Aqsa Mosque in Jerusalem. These fears are a root of the violence, the Prime Minister said.
Ban added he also has been "deeply troubled by statements by Palestinian militant groups, including Hamas and Islamic Jihad, praising such heinous attacks." But he did not include Abbas in that group.
"Israelis and Palestinians stand on the brink of another catastrophic period of violence. We need to keep the situation from escalating into a religious conflict with potential regional implications. We must create conditions for meaningful negotiations that will end the occupation and realize the aspirations of both peoples," the secretary-general said.
Hamas leader arrested
The highest-profile arrest so far in this recent spate of violence is Hassan Yousef, a leader of Hamas.
The Israel Defense Forces arrested Yousef on Tuesday.
The IDF did not link Yousef directly to any of the recent attacks against Israelis, but accused him of "actively instigating terrorism and publicly encouraging and praising the execution of attacks against Israelis."
"When you encourage, promote and praise the death of the innocent the IDF will act swiftly in order to contain the hateful incitement that jeopardizes the safety and well-being of so many Israelis and Palestinians alike," IDF spokesman Lt. Col. Peter Lerner said in a statement.
Tensions over holy site
Palestinian anger has been fueled in part by tensions over a Jerusalem holy site that is revered by both sides.
In recent years, hard-line Jewish activists have increasingly demanded greater access to the site, known as the Temple Mount by Jews and the Noble Sanctuary by Muslims.
Jews are not allowed to pray on the Temple Mount, where the al-Aqsa Mosque and Dome of the Rock are situated, but right-wing Israeli politicians have called for that to change.
That has set off widespread concern among Palestinians that the status quo is being undermined and that division of the site is coming -- a claim the Israeli government has repeatedly denied.
"The Temple Mount is being held hostage by people who want to bring about a religious war. We cannot allow this. Israel has no war with Islam," Israeli President Reuven Rivlin said Tuesday.
The upsurge in violent attacks and clashes between Israeli security forces and Palestinian protesters around the area has prompted Israel to repeatedly restrict Palestinians' access to the holy site.
Since the start of October, 45 Palestinians have been killed by Israeli security forces in the West Bank, Jerusalem and Gaza, according to the Palestinian Health Ministry. About 1,850 others have been wounded by live ammunition, rubber bullets and beatings, it said.
Israelis have been on edge as well.
On Tuesday, an Israeli man's vehicle was hit by rocks as he drove out of Kiryat Arba, a Jewish settlement in the West Bank, Israeli EMS spokesman Zaki Heller said. The driver stopped and got out, at which point he was killed when a truck with a West Bank license plate drove over him, Heller said.
But exactly what happened remained unclear. A photographer for The Associated Press who witnessed the incident shot photos of the Israeli man holding a large stick and walking toward a truck. The IDF said troops didn't arrive until after the incident and are investigating.
Also on Tuesday, an Israeli soldier was wounded when two suspects approached a military post in Hebron, according to the IDF, which later reported the two suspected assailants had been killed.
Deepening anger and mistrust
The spiral of violence
appears to be deepening the hostility and mistrust between the sides.
Many of the attacks on Israelis are believed to have been carried out by individual Palestinian youths unaffiliated with established militant groups. The attackers may have been motivated by what they saw on Facebook and Twitter, where photos and video of attacks are posted.
In his video message, Ban told young Palestinians that he understood their frustration.
"I know your hopes for peace have been dashed countless times. You are angry at the continued occupation and expansion of settlements," he said. "Many of you are disappointed in your leaders and in us, the international community, because of our inability to end this occupation."
But Ban urged them to "put down the weapons of despair "and push for a political solution.
To Israeli people and leaders, the secretary-general said he appreciated their concern about security and their anger over the attacks.
"But walls, checkpoints, harsh responses by the security forces and house demolitions cannot sustain the peace and safety that you need and must have," he warned.