Israel’s defense minister has signaled that Israeli ground forces could advance on Rafah — one of the last southern cities in the Gaza Strip that Israeli ground forces have not yet reached — raising concerns in a corner of the enclave where hundreds of thousands of people have crowded for shelter from the war.

“We are completing the mission in Khan Younis, and we will reach Rafah as well, and eliminate every terrorist there who threatens to harm us,” the defense minister, Yoav Gallant, said during a visit to troops in Khan Younis, according to footage distributed by his office late Thursday.

It was not clear whether Gallant’s comments reflected an immediate military objective or were intended more as a signal of resolve to the Israeli public and to Hamas as Israel awaits the armed group’s response to a proposed initial framework for a cease-fire and release of more Israeli hostages from Gaza.

Prime Minister Benjamin Netanyahu has insisted that Israel will continue fighting Hamas in the Gaza Strip until “complete victory,” even as he faces rising domestic pressure to make a deal to free the hostages and international calls to ease the fighting and limit harm to civilians.

Thousands of Palestinians have fled south in recent days to escape the fighting in Khan Younis and central Gaza, many with just the clothes they were wearing. The United Nations has described dire conditions in Khan Younis, where Israel has engaged in intense urban fighting as it says it is trying to kill or capture Hamas leaders it believes are hiding in and beneath the city in an extensive network of tunnels.

About half of Gaza’s 2.3 million people have crammed into the area surrounding Rafah, a city at the enclave’s southern border where about 200,000 lived before the war, the United Nations said on Friday.

Israel’s stated goal of toppling Hamas’ rule in Gaza would most likely require at least some of its forces to enter Rafah to attack the group’s network there.

If Israel were to advance on Rafah, it is not clear how it would provide for the safety of civilians, many of whom have fled multiple times as Israel has called for evacuations of areas it intended to target.

Jens Laerke, a spokesperson for the U.N. Office for the Coordination of Humanitarian Affairs, said the agency was deeply concerned about escalating combat in Khan Younis and the rise in displaced Gazans fleeing for Rafah.

“Rafah is a pressure cooker of despair, and we fear for what comes next,” Laerke told journalists in Geneva on Friday.

Severe constraints on deliveries of supplies such as food, water and medicine, and escalating levels of disease have increased the sense of desperation, Laerke said. “Every week we think it can’t get any worse,” he added. “Well, go figure, it gets worse.”

Netanyahu has said that Israel must take control of a strip of land along Gaza’s southern border with Egypt to defeat Hamas. The move effectively could cut Egypt off from Gaza, potentially weakening Egypt’s regional role and bringing the fighting directly to its border.

Egyptian officials have said Israeli military control of the land corridor would violate agreements between the two sides.

“It must be strictly emphasized that any Israeli move in this direction will lead to a serious threat to Egyptian-Israeli relations,” Diaa Rashwan, an Egyptian government spokesperson, said in late January.