In the message, delivered by Netanyahu's personal envoy Yitzhak Molcho, the Israeli Premier said that Israel will look into the death of Ziad Abu Ein, who is in charge of the Israeli settlements file at the Palestine Liberation Organization (PLO).
Abu Ein died on Wednesday after suffocating on teargas used by Israeli troops to disperse an anti-occupation demonstration in the northern West Bank town of Turmus Ayya.
Dozens of other demonstrators suffered temporary asphyxiation after inhaling excessive amounts of teargas.
Abbas has denounced the Israeli attack on Abu Ein as "barbaric" and declared a three-day mourning period.
The Palestinian leader said during a meeting of the Palestinian Authority that "all options remain open" following Abu Ein's death.
The Israeli army, meanwhile, has since said it was reviewing the circumstances of Abu Ein's participation in the protest and his subsequent death.