"In my speech to the General Assembly, I will refute the lies that are being told about us and I will tell the truth about our state and the heroic soldiers of the IDF, the most moral army in the world," Netanyahu said on the tarmac at Ben Gurion airport near Tel Aviv before boarding the plane.
In a Friday address to the UN General Assembly, Abbas accused Israel of carrying out a "genocidal crime" in its 50-day war against Gaza militants in which nearly 2,200 Palestinians, mostly civilians, were killed. Among those killed by Israeli forces, at least 577 were aged 18 or younger.
Speaking at the UN General Assembly in New York, Abbas said: "There is an occupation that must end now. There is a people that must be freed immediately.”
"The hour of independence of the state of Palestine has arrived."
He did not set a deadline for fast-tracking to Palestinian statehood, after aides suggested they were eyeing 2017 as a possible date.
Describing the latest Israeli assault on Gaza as a "genocidal crime," Abbas pledged: "We will not forget and we will not forgive, and we will not allow war criminals to escape punishment."
The war in Gaza was "a series of absolute war crimes carried out before the eyes and ears of the entire world," he said, citing the destruction left behind and the deaths of more than 500 children.
Earlier, an official from Netanyahu's office called the Palestinian leader's remarks "an inciteful hate speech full of lies," with Netanyahu pledging to refute it along with claims laid out in the UN speech of Iranian President Hassan Rouhani.
"After the Iranian president's deceptive speech and Abu Mazen's inciteful speech, I will tell the truth on behalf of Israel's citizens to the entire world," he said in a statement late Saturday, using Abbas's nickname.
"In my UN General Assembly speech and in all of my meetings I will represent the citizens of Israel and will -- on their behalf -- refute the slander and lies directed at our country," Netanyahu said.
Netanyahu will deliver his speech to the General Assembly on Monday, then will travel to Washington to meet US President Barack Obama at the White House on Wednesday.
On Saturday, the US State Department reacted to Abbas's speech with a tersely worded statement, calling the speech provocative and saying it would undermine peace efforts.
"President Abbas' speech today included offensive characterizations that were deeply disappointing and which we reject," said spokeswoman Jen Psaki.
"Such provocative statements are counterproductive and undermine efforts to create a positive atmosphere and restore trust between the parties," she said.
Psaki did not mention how Israel’s decades-long oppression of Palestinians and occupation of Palestinian territories undermine trust or efforts for a peace agreement.
Abbas spoke after rival Palestinian factions reached a unity deal that will pave the way for the return of the Palestinian Authority to Gaza and for a massive internationally funded reconstruction effort to begin.
The war in Gaza ended on August 26 when the two sides agreed in Cairo on a ceasefire and to hold future talks on Palestinian demands to end an eight-year blockade of Gaza.
(AFP, Al-Akhbar)