The Palestinian president reached out to Israel, saying he opposes near-daily Palestinian attacks on Israelis and suggesting the violence would stop if the defunct peace process resumes again.
Mahmoud Abbas made the remarks on Thursday in an interview with Israeli Channel 2 TV's Uvda program.
Israel has accused him of failing to condemn the wave of Palestinian attacks on Israeli civilians and security forces that erupted in mid-September.
The attacks, mostly stabbings but also shootings and car-ramming assaults, have killed 28 Israelis and two Americans.
Over the same time, at least 188 Palestinians have died by Israeli fire. Israel says most were attackers, and the rest died in clashes with Israeli security forces.
Abbas said the violence stems from "lack of hope, lack of trust" in Prime Minister Benjamin Netanyahu's commitment to a two-state solution to the conflict.
The Palestinian president also said that if peace talks resume, it would "give my people hope and nobody would dare go and stab or shoot".
US mediated Israeli-Palestinian peace talks collapsed in 2014.
In the interview, Abbas called on Netanyahu to meet with him "at any time".
"I want to see peace in my life," he said.
As for the current situation, he said the security co-operation between the Israeli military and Palestinian security forces continues and that if it were not for his forces, the violence would be much bloodier now.
He added that Palestinian security forces have raided schools and confiscated knives from students and told them not to carry out attacks.
Earlier on Thursday, the Israeli military demolished the home of a Palestinian man who fatally stabbed an Israeli civilian in the West Bank city of Hebron late last year.
The Palestinian, Ehab Maswada, stabbed the Israeli, Gennady Kaufman, outside a site holy to Jews and Muslims. Maswada was then shot and killed by officers at the scene.
Israel says home demolitions are an effective tool to deter attacks, but critics say the tactic amounts to collective punishment.
