The speech was delivered in Hebrew in an effort to reach out to Israelis. He made a point of not mentioning the Palestinians.
"I am not blinded by titles of kingmaker," Abbas said. "I don't want to be part of a bloc on the Right or Left. I am my own bloc."
Abbas said he was reaching out his arm toward coexistence.
"What unites us is stronger than what divides us," he said. "The time has come for listening to others."
Prime Minister Benjamin Netanyahu's allies in the Religious Zionist Party have vetoed a government that relies on Abbas and his Ra'am (United Arab List) Party. But Abbas said he had no problem with them.
"I have not ruled out anyone," Abbas said. "My approach is what yes, not what no."
Religious Zionist Pary MK-elect Itamar Ben-Gvir said he had not changed his mind, that Ra'am's connection to the Islamic Movement that supports Hamas cannot be forgotten and that Abbas cannot make himself into a "Teddy bear."
"A coalition relying on Ra'am would be the end of the Right," Ben-Gvir warned.