South Africa has submitted an "urgent request" to The Hague to consider if Israel's operations targeting Rafah are a breach of court orders.
Last month, the International Court of Justice (ICJ) ordered Israel to do all it can to prevent the deaths of Palestinian civilians, after South Africa accused its military of genocide in Gaza.
With Israel's forces threatening a ground invasion of the southern Gazan city of Rafah - where 1.4 million Palestinians have fled - South Africa has sent a follow-up request.
"The South African government said it was gravely concerned that the unprecedented military offensive against Rafah... has already led to and will result in further large-scale killing," a statement issued by South Africa's presidency said.
The court has not yet ruled on the core of the case brought by South Africa - whether genocide has occurred in Gaza - but it has recognised the right of Palestinians to be protected from acts of genocide.
In past cases, the ICJ has sometimes granted additional emergency measures when circumstances on the ground changed.
Vast swathes of Gaza have been flattened, with about 80% of the population displaced and a humanitarian catastrophe pushing more than a quarter of Palestinians towards starvation.
Israeli Prime Minister Benjamin Netanyahu has vowed to press on until "total victory" and insisted that military pressure will secure freedom for remaining hostages taken by Hamas in its 7 October attack.
His allies have said this idea is supported by a rescue mission of Israeli hostages in Rafah - but Fernando Marman, 60, and Louis Har, 70, were only the second and third captives freed by the Israeli military since the war erupted.
Other Israeli officials have said only a deal can bring about the release of so many hostages.
Progress on deal
There was said to be progress on talks over such a deal earlier on Tuesday, as key meetings continue between the sides in the Egyptian capital of Cairo.
A deal would give people in Gaza desperately needed respite from the war, now in its fifth month, and offer freedom for at least some of the 100 people still held captive in Gaza.
A Western diplomat said a six-week deal is on the table but warned that more work is still needed to reach an agreement.
Israel has proposed a two-month ceasefire in which hostages would be freed in exchange for the release of Palestinians imprisoned by Israel.
Top Hamas leaders in Gaza would also be allowed to relocate to other countries - but the militants rejected these terms.
Instead, they laid out a three-phase plan of 45 days each in which the hostages would be released in stages.
In return, Israel would free hundreds of imprisoned Palestinians, including senior militants, and the war would be wound down with Israel withdrawing its troops.
That was viewed as a non-starter by Israel, which wants to topple Hamas before ending the war.