His comments came as Prime Minister Benjamin Netanyahu pledged a crackdown and Israel, in a show of force, demolished the homes of two Palestinians who carried out attacks last year.
More clashes also erupted Tuesday, including in Bethlehem following the funeral of a 13-year-old killed by Israeli soldiers during rioting outside the city.
"We don't want a military and security escalation with Israel," Abbas said at a meeting of Palestinian officials, according to official news agency Wafa.
Abbas's intentions were unclear before his recent comments, particularly following his UN General Assembly speech last week, in which he declared he was no longer bound by accords with Israel.
But the question remains of whether Palestinian youths frustrated with both Abbas's leadership and Israel's right-wing government will listen to his appeals.
Today's demolitions came with Netanyahu under increasing pressure from right-wing members of his coalition, which holds only a one-seat parliamentary majority, as clashes have spread following the murder of four Israelis.
The houses destroyed were the former homes of Ghassan Abu Jamal and Mohammed Jaabis, the military said. They were placed under demolition orders after the men attacked Israelis last year.
Armed with meat cleavers and a pistol, Abu Jamal and his cousin Uday Abu Jamal killed four rabbis and a policeman before being shot dead in November 2014.
Jaabis rammed an earthmover into a bus in August 2014, killing an Israeli and wounding several others before he was shot dead by police.
Yasser Abdu, 40, a neighbour and friend of the Abu Jamals, accused Israel of a "policy of collective punishment.
