And even after that, the military kept a veil over its activity. On Monday it released only limited information, conveying the impression of a controlled, low-intensity advance.

Mr. Netanyahu, speaking to reporters, emphatically rejected appeals for a cease-fire as “calls for Israel to surrender to Hamas, to surrender to terrorism.” Asked about the death toll in Gaza, Mr. Netanyahu said that “not a single civilian has to die,” and he accused Hamas of “preventing them from leaving the areas of conflict.”

The military released unverified footage that appeared to show Israeli tanks moving slowly down beaches in northern Gaza. The clips also showed Israeli bulldozers reshaping the terrain, possibly to ease the tanks’ passage or to destroy tunnel infrastructure. But the footage showed little actual fighting, and reports of clashes were limited to terse and vague statements.

After international condemnation of the toll the attacks have taken on Palestinian civilians, Israel has spoken only of its actions against Hamas fighters.

“Troops killed dozens of terrorists who barricaded themselves in buildings and tunnels,” read one announcement from the Israeli military.

Hamas has also tried to turn vagueness to its advantage. Its military wing has acknowledged clashing with Israeli troops, but also only in general terms. “Mujahedeen surprise enemy forces advancing northwest of Beit Lahia,” said one Hamas statement on Monday afternoon.

By Monday evening, it appeared that the Israeli soldiers were encircling Gaza City, sealing off access to the city from the north and south, but still refraining from sending major forces inside it.

“A sort of pincer movement, cutting it off and making sure nobody leaves,” is how Dr. Krieg described it.

Whether it will work is unclear: The real test will come once the Israeli forces enter Gaza City.

“We’re not in the urban combat stage yet, where it becomes very, very messy,” Dr. Krieg said.