"We will continue to support all efforts to create the conditions to make meaningful negotiations possible," Ban told journalists after meeting Abbas in the West Bank city of Ramallah.
"But ultimately it is for Palestinians and Israelis to choose peace. Our most urgent challenge is to stop the current wave of violence and avoid any further loss of life."
Ban, who met Israeli Prime Minister Benjamin Netanyahu yesterday, said that "the only way to end the violence is through real and visible progress toward a political solution, including an end of the occupation".
Abbas called on Israel to strictly respect rules governing Jerusalem's flashpoint Al-Aqsa mosque compound, known to Jews as the Temple Mount.
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Clashes between Israeli security forces and Palestinian protesters at the compound in September preceded the current wave of violence.
Netanyahu has repeatedly accused Abbas of inciting violence by suggesting that Israel wants to change the status of the compound.
Muslims fear Israel will seek to change rules governing the site, located in Israeli-annexed east Jerusalem.
"The continued occupation and aggression against Christian and Muslim holy sites in east Jerusalem, particularly against Al-Aqsa, opens the door to a religious conflict, which has unfortunately started," Abbas told journalists.
"We don't want it and we are warning over its consequences."
Three weeks of attacks and unrest have raised fears of a full-scale Palestinian uprising.
More than 40 Palestinians have been killed in the upsurge in violence that began at the start of the month, including alleged attackers. Eight Israelis have died in attacks.
Many of the attackers have been young Palestinians who appear to be acting alone. Most incidents have seen the attackers stab Israelis before being shot dead.