Some police were deployed overnight, but Nour Odeh, Al Jazeera's Gaza correspondent, said that Hani al-Qawasmi, the Palestinian interior minister who recently resigned, still wanted assurances.
Odeh said that al-Qawasmi had reiterated that if he were to stay on in his post he would want to be supplied with a budget and to receive assurances from security chiefs that they would report to him.
Odeh said that recently: "The situation [in Gaza] on the ground has reached the point of being completely out of control. The deployment and checkpoints ... are raising hopes that just maybe ... with the agreement ... law and order will begin to be restored. But it is a long way from this at this point."
Nabil Shaath, a senior Fatah leader and close Abbas aide, said the policemen provided under the agreement will now take orders from the interior ministry under the unity government.
He said: "There is a full agreement. The determination is there and I think what we will see in the next 48 hours is a full deployment to deal with the lawlessness in the Gaza Strip."
"The new government should show signs of maturity and responsibility"
Husky, Ottawa, Canada
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Previous police deployments in Gaza have not fully secured the territory.
Human rights groups say about 400 Palestinians have died in street fights in the city over the past year.
Separately, Gaza residents reported seeing Israeli tanks and bulldozers crossing the border on Wednesday.
Israel has denied the report, amid rising tensions from cross-border rocket fire since last week.
The salvoes have persisted despite an Israeli-Palestinian truce struck in November, usually at the hands of groups which say they were not bound by that deal.
Palestinians say Israel's continued military actions in the occupied West Bank – where the truce does not apply - provoke attacks from Gaza.
"In such climate it is difficult to have a national dialogue about a ceasefire with Israel," Shaath said.
Israel has proposed making part of Gaza near the border a no-go zone, and some Palestinians there now fear losing their homes.