"For your own safety, you are required to immediately evacuate your homes and move toward Gaza City centre," the one-page Arabic-language leaflet said.
The message directed residents to use specific roads to move out of their neighbourhoods, which form a crescent around the southern half of the city centre.
The leaflets were dropped shortly before Gaza health officials said a new wave of Israeli air strikes killed five people and wounded two others.
Among the districts named were Sheikh Ajlin, Tel al-Hawa, Rimal, Zeitun, Shejaiya-Turkman and Shejaiya-Jadida.
The message gave no reason for the order but pledged that everyone who complied would be safe.
"This is a temporary confrontation. In the end, everyone will go home," the leaflet said on the seventh-day of Israel's fiercest assault on the coastal enclave in four years.
"In keeping with Israel Defence Forces (army) regulations, all civilians will be kept from harm's way."
A military statement confirmed that two sets of leaflets were dropped across various districts of Gaza City with specific instructions about where residents should go.
But the statement failed to mention the security pledge to civilians or the reference to a "temporary" campaign.
An army spokeswoman said leaflets had been dropped over Gaza on previous occasions during the current offensive but did not say why they were dropped on this occasion as well.
The latest drop came as Hamas militants fired a long-range rocket at Jerusalem that landed just 15 kilometres (nine miles) south of the Holy City.
It came as Israel weighed whether to expand its aerial campaign into a ground incursion or agree to an Egyptian-mediated ceasefire being put together through indirect talks between Israeli and Hamas officials in Cairo.
A senior Israeli official earlier Tuesday said the leadership had decided to postpone a decision on a ground operation "to give diplomacy a chance to succeed."