Erekat said the Palestinian leadership should prepare a new constitution, reconcile with Hamas and seek membership in United Nations agencies, The Jerusalem Post reported.
He said steps were under way to seek membership in 17 U.N. agencies and organizations, including the International Criminal Court, the World Health Organization, World Bank and UNESCO, the newspaper said.
Peres was criticized at the annual conference of Israel's ambassadors after he declared the only solution to the Israeli-Palestinian conflict is a two-state plan.
"Deep changes are occurring in the Arab world and Israel ... may adopt a passive position in which reality will determine decisions, or Israel can take the initiative and with courageous steps make a positive effect ... , Peres said.
He said a first step is "completing the peace process with the Palestinians without further delay".
Peres said there is "a clear majority among the public supporting a two-state solution."
He said he has known Abbas for 30 years.
"We don't have to agree with every word and every act without criticizing them, but I am aware of the reality in which [Abbas] is the only Arab leader who stated publicly that he supports peace and is against terror. ... One must say with integrity that whoever does not want a two-state solution must offer an alternative solution, what will be instead? What is the future of the state of Israel? Otherwise, reality will force a solution upon us, not us," Peres said.
Commenting on Peres' statements, Abbas said the Palestinians do not seek to meddle in Israel's internal affairs but seek "a partner that believes in peace," Ynetnews.com reported. "We want to live as a state alongside Israel, which we've already recognized," he said.
The Likud-Beitenu party issued a statement chiding Peres.
"It's very unfortunate that the president chose to express a personal political view that is detached from public opinion when it comes to Abbas, who refuses to make peace," the statement said.
"It is even more unfortunate that the president chose to present a political stance that encourages criticism of Israel in front of foreign ambassadors."
Labor Party leader Shelly Yacimovich accused the Likud-Beitenu party of crossing a red line.
"Saying that Peres encourages criticism of Israel in the world is low. Peres stops attacks on Israel with his own body. He is our best ambassador," Yacimovich said.
Notable deaths of 2014 [PHOTOS]