TEL AVIV—Israeli tanks and infantry pushed into the outskirts of Gaza City and temporarily blocked one of the main roads connecting the northern part of the Gaza Strip to the south, a major advance that appeared aimed at encircling the enclave’s biggest population center.

Israeli ground troops entered Gaza late last week, starting a new phase in its war to eradicate Islamist militant group Hamas. Hamas fighters killed around 1,400 people and took more than 220 hostages in a series of attacks inside Israel earlier this month.