Karim Abu Shaban, 21, of Gaza City said he and his neighbors all had gotten such calls. His first caller had an Egyptian accent. “Oh, God help you, God be with you,” the caller began.

“It started very supportive,” Mr. Shaban said, then the questions started. The next call came in five minutes later. That caller had an Algerian accent and asked if he had reached Gaza. Mr. Shaban said he answered, “No, Tel Aviv,” and hung up.

Interviews last week with senior Israeli intelligence and military officers, both active and retired, as well as with military experts and residents of Gaza itself, made it clear that the battle, waged among civilians and between enemies who had long prepared for this fight, is now a slow, nasty business of asymmetrical urban warfare. Gaza’s civilians, who cannot flee because the borders are closed, are “the meat in the sandwich,” as one United Nations worker said, requesting anonymity.

It is also clear that both sides are evolving tactics to the new battlefield, then adjusting them quickly.

To that end, Israeli intelligence is detaining large numbers of young Gazan men to interrogate them for local knowledge and Hamas tactics. Last week, Israel captured a hand-drawn Hamas map in a house in Al Atatra, near Beit Lahiya, which showed planned defensive positions for the neighborhood, mine and booby trap placements, including a rigged gasoline station, and directions for snipers to shoot next to a mosque. Numerous tunnels were marked.

A new Israeli weapon, meanwhile, is tailored to the Hamas tactic of asking civilians to stand on the roofs of buildings so Israeli pilots will not bomb. The Israelis are countering with a missile designed, paradoxically, not to explode. They aim the missiles at empty areas of the roofs to frighten residents into leaving the buildings, a tactic called “a knock on the roof.”

But the most important strategic decision the Israelis have made so far, according to senior military officers and analysts, is to approach their incursion as a war, not a police operation.