The people were killed in two separate incidents Monday morning, both times "by Israeli gunfire as they were returning to check on their homes in the Al-Shaaf area, east of Al-Tuffah neighborhood, in the east of Gaza City", said Mahmud Bassal, spokesman for the rescue service, which operates under Hamas authority.

Israel's military said it had fired at militants who crossed the so-called "Yellow Line" and approached troops in the Shujaiya neighbourhood, which is adjacent to Al-Tuffah.

The Yellow Line is the boundary behind which Israeli troops pulled back and remain stationed under the ceasefire agreement with Hamas.

Several such incidents have taken place since a fragile US-brokered ceasefire began on October 10, with 80 people killed in total, according to Gaza's Hamas-run health ministry.

The Israeli military struck dozens of Hamas positions across Gaza on Sunday after two soldiers were killed in combat, with Israel accusing the group of "a blatant violation" of the truce.

Hamas denied knowledge of any attack, and one official accused Israel of fabricating "pretexts" to resume the war.

Hundreds of thousands of Palestinians have returned to Gaza's north since the beginning of the ceasefire, often coming home to piles of rubble where their homes once stood.