European foreign ministers pressed their Israeli counterpart on Monday to agree to the creation of a Palestinian state, in a meeting that left European diplomats bewildered about postwar Israeli plans for the Gaza Strip and reinforced the deep disconnect between Israel and much of the world.

The two sides appeared to be having two different conversations. Josep Borrell Fontelles, the European Union’s top diplomat, said after the meeting in Brussels that European nations were resolute that “sustainable, lasting peace” must include Palestinian statehood, an option that Prime Minister Benjamin Netanyahu of Israel has doubled down on opposing in recent days.

Israel’s foreign minister, Yisrael Katz, presented to the Europeans a plan involving an artificial island off Gaza’s coast — a plan that did not address the future governance of the territory, according to officials in the meeting.

While the diplomats talked past each other, heavy fighting intensified in southern Gaza on Monday, with medical personnel reporting major exchanges of gunfire and a surge of Israeli tanks and troops into areas around hospitals.