"This is genocide – the murder of entire families is genocide committed by Israel against the Palestinian people," he said at an emergency meeting of the Palestinian leadership in Ramallah.
"What is happening is a war against the Palestinian people as a whole, and not against the (militant) factions," he has said.
"We know that Israel is not defending itself, it is defending settlements, its main project," said Abbas.
"We are moving in several directions to stop the Israeli aggression and spilling of Palestinian blood, including talking to Egyptian President (Abdel Fattah) al-Sisi and UN Secretary General Ban Ki-moon."
Palestinian Hamas leader Khaled Mashaal gave a live address in which he said that “the abduction of the three teens in the West Bank is part of the Palestinian rage. That was a starting point. We will fire on Haifa if occupation does not stop."
Egypt on Wednesday urged Israel and Hamas in Gaza to halt their spiraling conflict but played down hopes of a Cairo-mediated truce.
"There is no mediation, in the common sense of the word," said Egyptian foreign ministry spokesman Badr Abdelatty.
"Egyptian diplomatic efforts are aimed at immediately stopping Israeli aggression and ending all mutual violence. (Egyptian) contacts have not yet achieved a result."
Egypt, which borders both Israel and Gaza and was the first Arab country to sign a peace treaty with Israel in 1979, has often played an intermediary role between Israel and Hamas.
Israel warplanes have so far hit 550 targets in Gaza, and Hamas militants have hit back with 165 rockets, some of which struck Jerusalem and Tel Aviv and as far away as Hadera, 116 kilometers (72 miles) to the north of the coastal enclave.
Palestinian fatalities include militants but also women and children. More than 370 people have been wounded.