The mutual accusations came amid growing discontent in the Gaza Strip with Hamas over its failure to improve the living conditions of its residents.
Abbas will meet with local residents and officials and receive a briefing about efforts to "rebuild" the city and its refugee camp.
The Palestinian Authority has come under attack for failing to order its security forces to engage IDF soldiers and settlers.
IDF, Palestinian reports disagree about alleged second casualty
Israeli media, citing Palestinian reports, stated that a Palestinian photojournalist was seriously injured by IDF fire during the night's clashes.
One of the victims is a 3-year-old toddler who is currently in critical condition.
Hamas, for its part, views the results of the elections as a vote of confidence in its ideology and armed “resistance” against Israel.
About five people were injured in the incident, with one Palestinian security officer in severe condition after being shot in the head.
Last week, the Hamas-affiliated Islamic Bloc won in the elections for the student council at An-Najah University in Nablus, the largest Palestinian university in the West Bank.
The Palestinian Authority is not looking for a quick fix, or a delay, but rather an end to settlement activity