Tension between Israel and militant groups in Gaza has been going on for 11 days since May 10, leaving over 255 Palestinians dead and hundreds injured, as well as huge destruction of buildings and infrastructure, reports Xinhua news agency.
Abbas made the accusation at an emergency meeting on Wednesday of the Arab Parliament of the Arab League, which was held to discuss the ongoing tension in Gaza.
His speech was also aired on the official Palestine television.
"What Israel does now in the Gaza Strip is a state terror and war crimes that violate international law," Abbas said.
"We will prosecute Israel before the international courts."
Palestine "is seriously working with all parties to pressure Israel to stop its aggression on our people not only in the Gaza Strip, but also in the West Bank and East Jerusalem", he added.
Abbas revealed that Palestine has informed the US of its full readiness to work through the international Quartet to end wars and achieve peace in the Middle East.
According to the latest data by the UN Office for the Coordination of Humanitarian Affairs (OCHA), 219 Palestinians, including 63 children, were killed in Gaza.
In the West Bank, 25 Palestinian deaths were tallied, including four children.
Israeli sources reported 12 people killed, including two children and a soldier.
Thousands of people are injured, mainly in the West Bank and in Gaza.
Militant groups fired barrages of rockets from the Gaza Strip at Israel, while Israeli fighter jets kept carrying out intensive airstrikes on buildings and infrastructure in the besieged enclave.