“It has become increasingly clear that Israel’s actions in Rafah are part of the end game in which Gaza is utterly destroyed as an area capable of human habitation,” Vaughan Lowe, a British lawyer, told the court. “This is the last step in the destruction of Gaza and its Palestinian people.”

Mr. Lowe was part of the South African legal team that presented its case over two hours on Thursday.

South Africa’s filings said the rights of Palestinians in Gaza were under threat, adding that Israel’s control over two major border crossings in southern Gaza — at Rafah and at Kerem Shalom — put at extreme risk the flow of humanitarian supplies into Gaza and the ability for hospitals there to function.

“It is difficult to imagine such a situation could get worse, but, unfortunately, it has,” John Dugard, another member of the South African team, told the court.

Several members of the team addressed the court in an attempt to build their case, quoting frequently from warnings by senior United Nations officials that an assault on Rafah would worsen conditions for civilians and the enclave’s hunger crisis.

One member of South African legal team, Tembeka Ngcukaitobi, quoted statements by senior Israeli officials that he said showed an intent to destroy Gaza as a whole and not simply Hamas, the country’s stated enemy.

The legal team also asked the court to order Israel to facilitate access to Gaza for aid workers, investigators, fact-finding missions and journalists.

One of the lawyers, Adila Hassim, showed the court a photo of shattered buildings in Khan Younis, a city north of Rafah, to illustrate the devastation caused by Israel’s military in Gaza as a whole. Ms. Hassim appeared to be on the verge of tears as she described the deaths of children in the military campaign.

Israel has vehemently denied South Africa’s claims, repeating that it has placed no restrictions on the amount of aid entering the enclave and that it has taken steps recently to ramp up the amount of food and other supplies going in, including opening two crossing points in northern Gaza.

Israel has also said that its latest assault on eastern Rafah was a “precise operation” targeting only members of Hamas, the terrorist group that led the Oct. 7 attacks, which Israeli authorities say killed more than 1,200 Israelis and led to the capture of about 250 others.

Israel is expected to make its defense before the court on Friday. Gilad Noam, Israel’s deputy attorney general for international law, is among the officials in the Israeli delegation who are expected to address the court. It was not clear when the court would issue a decision, but given that South Africa said on Thursday that its petition was extremely urgent because an assault on Rafah was ongoing, it appeared possible that a ruling could come soon.

The hearings are part of South Africa’s case accusing Israel of genocide, which it filed in December. In late January, the court ordered Israel to do more to prevent acts of genocide, but it stopped short of calling for a cease-fire. The main case, dealing with the accusation of genocide, is not expected to start until next year.

The court, established by the founding charter of the United Nations in 1945, was created to settle disputes between member states. It has no means of enforcing its orders, but the South Africa case has contributed to the international pressure on Israel to rein in its campaign in Gaza.

Marlise Simons and Johnatan Reiss contributed reporting.