"I contacted the Palestinian factions in Gaza and they want to reach calm, but Israel rejects reaching calm," Xinhua quoted Abbas in a televised speech.
Earlier Tuesday morning, Israel launched "Operation Protective Edge" in the Hamas-controlled Gaza to quell incessant rockets, projectiles and mortars fired from there into Israel.
Medics said 23 Palestinians, including six children, were killed and more than 122 injured, seven of whom in serious conditions, during intensive Israeli air strikes on Gaza Tuesday.
Hamas armed wing al-Qassam Brigades has, for the first time ever, claimed responsibility for launching long-range rockets that hit Israeli towns including Tel Aviv and Jerusalem.
Abbas assured that he will go to the international agencies "to stop the Israeli aggression on the Palestinian people", adding that "the unity government will do all its best to help the Palestinians in Gaza and Jerusalem".
"It is time that the international community bears its responsibility toward the Israeli aggression on our people," Abbas said in his speech.
The Palestinian state media reported Abbas had spoken over phone with Egyptian President Abdel-Fattah al- Sisi to discuss the growing tension in the Gaza Strip.
Sisi promised that Egypt will do its best to help bring calm in the Gaza Strip and avoid more Israeli strikes.