An explosion took place on Tuesday near the convoy of Palestinian Prime Minister Rami Hamdallah in Beit Hanoun, shortly after the convoy entered the Gaza Strip.
The attack on the Western-backed leader, who is spearheading the Authority's reconciliation efforts with Gaza's dominant group, Hamas, happened on the day the White House is due to hold a meeting on the humanitarian situation in the enclave.
Hamas seized power of Gaza in 2007, and repeated attempts to reconcile with the Palestinian Authority have failed or stalled.
Hussein Al-Shaikh, member of Abbas' Fatah party, said in a press statement that "the grave criminal act is an unprecedented act and will have grave consequences".
Furthermore, Azzam al-Ahmad, a member of the Central Committee of Fateh movement said that President Abbas, who is now visiting King Abdullah of Jordan, has chose to return to the West Bank.More news: Why NASA has suspended People's Assembly agenda
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The Palestinian Authority has accused militants in Gaza of trying to kill Hamdallah.
Three vehicles of his convoy were damaged and one had signs of blood on its door, AP reported.
The top Palestinian Authority officials made the rare trip from the West Bank for the inauguration of a desalination plant.
This ambitious project has received funding from the World Bank, European Union, and other European governments.
Greenblatt has several times in recent weeks condemned Gaza's Hamas terrorist rulers for spending their aid money on terror tunnels and rocket attacks instead of on Gazans.