About 50 tanks, accompanied by bulldozers, pushed into an area near the Gaza-Egypt border before dawn on Thursday, taking up positions near the long-closed Gaza airport, residents and Palestinian security officials said.
The forces advanced about 8km, the furthest since the offensive began in late June, blocking a main highway and the eastern entrance to Rafah, a town on the Egyptian border.
As the tanks took up positions, Israeli aircraft fired missiles at four groups of gunmen, killing four.
Twenty-six Palestinians were wounded in the air strikes, ten of them fighters, security and hospital officials said.
Troops also carried out house-to-house searches in Rafah.
Later, forces fired a tank shell at residents gathering in the area after daybreak, killing a boy and wounding three people, one a 4-year-old girl, hospital and security officials said. The boy is reported to be either eight or ten years old.
Three more bodies were brought to the hospital early on Thursday, but the circumstances of their death and whether they were fighters were not immediately clear.
The Israeli army confirmed its forces were operating in southern Gaza and said the air strike came after its troops were targeted with a rocket-propelled grenade.
Israel has killed at least 158 Palestinians, more than half of them civilians, in Gaza since it began an offensive to stop gunmen from firing rockets into Israel and to pressure fighters to free a soldier that resistance groups captured on June 25.