Israel’s military said Tuesday that its ground operation in Gaza was at its “most intense day,” as it continued an offensive that has expanded to all of Gaza, not just the north of the territory.

Troops were pushing into Khan Younis, Gaza’s second-largest city, the Israel Defense Forces said.

IDF Chief of the General Staff Lt. Gen. Herzi Halevi said it was a “third phase” that targeted what he said were Hamas strongholds in the south.

The United Nations warned that “an even more hellish scenario is about to unfold” in southern Gaza. The offensive in the north involved orders for people to evacuate to the south, and the U.N.’s secretary-general said that people have nowhere safe to go.