Hamas said on Saturday that it was reviewing a new Israeli proposal for a cease-fire in the Gaza Strip, a move that comes amid efforts to break a deadlock in the talks between the armed group and Israel.

The statement came as anticipation was growing of an Israeli invasion of Rafah, a city in southern Gaza where more than a million people have been displaced. Humanitarian groups have warned that such an offensive would have catastrophic consequences for civilians.

In a statement, Khalil al-Hayya, a senior Hamas official, said the group had received an Israeli response to a proposal it delivered to Egyptian and Qatari mediators two weeks ago. Mr. al-Hayya did not provide any details included in the Israeli proposal, but he said Hamas would respond to it after the group finished studying it.

On Friday, a delegation of Egyptian officials visited Israel in an attempt to advance the negotiations between Israel and Hamas, according to an Israeli official familiar with the visit, who spoke on condition of anonymity because they were not authorized to communicate with the media.

In recent weeks, the negotiations aimed at achieving a cease-fire and the release of hostages held in Gaza have stalled amid disputes about an Israeli withdrawal of forces and the length of a halt in the fighting. Hamas has demanded a permanent cease-fire, whereas Israel has expressed openness to a temporary pause.

Another key sticking point is whether Israel will allow displaced Palestinians to return to the north. Hamas officials have said Palestinians should be able to go back en masse, while Israeli officials have said Israel wants to put limits on who can return, where and how.

The impasse has left Palestinians in Gaza to continue to suffer through Israel’s pulverizing bombing campaign, which has caused destruction throughout the territory and left more than 34,000 dead, according to the Gaza health ministry. The ministry’s figures do not differentiate between combatants and civilians.

It has also prevented Israeli hostages from reuniting with their families, many of whom have become increasingly critical of the Israeli government’s failure to secure their loved ones’ freedom.

Calls for cease-fire talks have gained urgency as Israel signals that it may go ahead with its invasion of Rafah. Earlier this week, an Israeli military official said that if Israel were to begin an invasion of Rafah, an Israeli-designated “humanitarian zone” along the coast would be expanded to take in more civilians. He spoke on condition of anonymity to discuss internal deliberations.

The comments were among the first indications of the Israeli military’s plans for civilians if it were to launch a major ground offensive in the area.

Secretary of State Antony J. Blinken is expected to travel to Israel next week, a trip that would come as the United States has urged Israel not to undertake a major military operation in Rafah.

Israeli officials have repeatedly said that entering Rafah was necessary in order to fight Hamas battalions there, but Israel’s allies have expressed grave concerns about what an invasion would mean for people who have crowded into the city, many of them living in makeshift tents in large encampments.