Abbas appreciated the Egyptian role and efforts to protect the Palestinian people, official Palestinian news agency Wafa reported.
The Palestinian president has also urged both parties to commit to the terms of the new ceasefire initiative to stop the Palestinian bloodshed, hoping that the new proposal would pave the way for a political process to end the occupation of Palestine and lead to the creation of an independent state.
Hamas officials have abstained from commenting on the Egyptian initiative, stating they are still studying the proposal.
Meanwhile, Israeli media reports confirmed that the Israeli mini-cabinet will convene on Tuesday to discuss the Egyptian initiative.
Earlier on Monday, Egypt has launched a ceasefire initiative between Israel and the Palestinian factions in the Gaza Strip, inviting both parties to stop hostilities by Tuesday at 0600 GMT.
The initiative urges both Israel and the Palestinians in Gaza " to stop all acts of aggression whether via land, sea or air" while opening border crossings to facilitate traffic of people and goods in the light of stable security conditions on the ground.
Last Tuesday, Israel launched an all-out aerial operation dubbed Protective Edge to end Gaza rocket fire into its territories, leaving 185 Palestinians killed and 1385 others injured.
The initiative includes holding separate talks with high profile Israeli and Palestinian delegates in Cairo within 48 hours from carrying out the initiative to address the required measures for building mutual trust.
The talks will be based on the 2012 truce brokered by Cairo.