GAZA CITY, Gaza — Israel ignored mounting international calls for a cease-fire Monday and said it won’t stop its crippling 10-day assault until “peace and tranquility” are achieved in southern Israeli towns in the line of Palestinian rocket fire.

Israeli forces seized control of high-rise buildings and attacked smuggling tunnels and several mosques in a campaign against Hamas militants that took an increasing toll on civilians: Three young brothers were reported killed during shelling, five people died in a house hit by ship fire, and Palestinian wounded filled hospital corridors.

Arab delegates met with the U.N. Security Council in New York Monday, urging members to adopt a resolution calling for an immediate end to the Israeli attacks and a permanent cease-fire. At the same time, diplomats and European leaders traveled the region in an effort to stop Israel’s expanding ground and air offensive.

In a serious urban clash, Israeli troops and Hamas militants fought a gunbattle on the outskirts of the crowded Gaza City neighborhood of Shajaiyeh, Israeli defense officials said. Details also emerged of an unsuccessful attempt by Hamas fighters to capture Israeli soldiers hours after the ground operation began Saturday with a withering round of artillery fire.