As the Israeli military stepped up pressure on what it calls Hamas’s last stronghold in Gaza, fighting elsewhere in the Palestinian enclave on Sunday led to warnings that the militants might remain a force for a long time to come.

Close-quarters ground combat between Hamas fighters and Israeli troops raged in parts of northern Gaza over the weekend, both sides said on Sunday, even as the world’s attention was largely focused on the southern city of Rafah, where Israel escalated military operations last week.

It has become a familiar scenario in the Gaza Strip over the course of the seven-month war: After pitched battles, Israel declares an area clear of Hamas, only to return after the militants reconstitute their forces.

On Sunday, Secretary of State Antony J. Blinken said he was concerned that Israel’s failure to lay down a template for the governance of Gaza meant that its victories might not be “sustainable” and would be followed by “chaos, by anarchy and ultimately by Hamas again.”

Mr. Blinken’s warning came as the Israeli military said its soldiers had “eliminated a number” of fighters in the Gaza City neighborhood of Zeitoun. In nearby Jabaliya, where civilians were ordered to evacuate on Saturday, troops went in overnight after fighter jets struck more than two dozen targets, the military said. The operation, it said, was “based on intelligence information regarding attempts by Hamas to reassemble.”

Hamas said on Sunday that its fighters were engaged in “fierce clashes” with Israeli soldiers near Jabaliya and that the fighters had fired heavy-caliber mortar shells at Israeli forces in Zeitoun.