"The upcoming government will obey my policy," he told members of the Palestine Liberation Organisation's Central Council. "I recognise Israel and reject violence and terrorism, and recognise international commitments."
Israel halted peace talks after a Wednesday reconciliation agreement between Abbas's PLO and the Islamist Hamas movement, which is pledged to Israel's destruction.
Abbas also stressed the Palestinians would never recognise Israel as the "Jewish state," saying the Palestinians recognised it as a state in 1993 and should not have to accept its religious identity.
Israeli Prime Minister Benjamin Netanyahu had repeatedly insisted on recognition of Israel as a Jewish state during the US-brokered peace talks.
Abbas spoke ahead of Palestinian crisis talks expected to focus on US peace efforts and the unity deal.