Dozens of Palestinians have died in outbreaks of violence between supporters of the two groups.
The Israeli diplomatic source gave no date for the Badr Brigade's planned deployment in Gaza.
"Basically, we have agreed, though it has not yet been officially released," the source said. "The request came through before the ceasefire, but certainly this [deployment] could boost the truce."
"We have agreed, though it has not yet been officially released"
Israeli diplomatic source
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Lieutenant-General Keith Dayton, the US security coordinator in the region, told an Israeli newspaper last week that the idea of redeploying the Badr Brigade "makes sense both from the military as well as from the political point of view".
Hamas has created its own militia in the Gaza Strip, the 6,000-strong "Executive Force".
After the truce was declared by Olmert and Abbas on Sunday, the Palestinian government posted thousands of police along the Gaza frontier to rockets being fired into Israel.
The ceasefire has not been extended to the occupied West Bank where Israeli military operations have continued.
On Tuesday, Israeli forces arrested 13 suspected Palestinian fighters, the army said.
Amir Peretz, the Israeli defence minister, said Israel required an end to Palestinian operations in the West Bank before it would consider a ceasefire there.
Ismail Haniya, the Palestinian prime minister, is on his first foreign trip since he took office in March.
He is visiting Egypt, Lebanon, Kuwait, Saudi Arabia, Qatar, Syria and Iran to seek political and financial support for the government.
Meanwhile, a senior Palestinian official said Abbas would meet Condoleezza Rice, the US secretary of state, in the West Bank on Thursday to discuss the truce in the Gaza Strip.
An Israeli source said there were no plans for her to meet Ehud Olmert, the Israeli prime minister.