Some political leaders in Israel have made no secret of their desire to see Hamas removed. Foreign Minister Tzipi Livni, head of the governing Kadima Party, has said that ousting Hamas was Israel's "long-term objective."
And Benjamin Netanyahu, the front-runner in the Israeli elections next month, warned, "In the long run, there won't be any other choice but to topple the Hamas government."
The Israeli leaders do not want Hamas to play a leading role in reconstruction.
"What we want to see is the reconstruction of Gaza. What we don't want to see is the reconstruction of Hamas," Mark Regev, spokesman for the Israeli government, told ABC News.
"It is important that the international community make sure that the reconstruction aid reaches the people of Gaza directly and that there will not be any mechanism to re-empower Hamas," Regev said.
To complicate the situation, Iran has been vocal in its desire to be involved in Gaza's reconstruction, airing plans to rebuild the Palestinian legislative council.
On Sunday, according to Iranian state television, parliamentary Chairman Ali Larijani said that Iran feels that it is its "duty to continue [its] endeavor to reconstruct the glorious Gaza" and that Iran "will undertake the reconstruction of the Palestinian parliament building in Gaza."
Abdallah said that Iran was using the Israeli-Palestinian confilct for its own purposes and "the coming era will not allow this to happen."
Meanwhile the United Nations Relief and Works Agency, on whose shoulders much of the reconstruction work will fall, objects to Israeli policy. "There will be no reconstruction unless Israel opens all crossing borders" into Gaza, which Israel blockaded after Hamas took power, spokesman Adnan Abu Hasnan said.
Aid organizations have millions of dollars set aside but cannot begin work without Israel's help.
The Associated Press contributed to this report.