•South Africa also called on the court to order Israel to cease military operations in Gaza.
•Israel will offer its defence on Friday, but has previously said its actions in the Gaza Strip are justified because it is responding to Hamas's deadly attacks on 7 October.
Israel's plan to "destroy" Gaza comes from "the highest level of state", the UN's top court has heard.
The claims were made by South African lawyers as it presented its case accusing Israel of genocide at the International Court of Justice.
South Africa also called on the court to order Israel to cease military operations in Gaza.
Israel - which will present its defence on Friday - has vehemently rejected the accusations as "baseless".
The court will deliver only an opinion on the genocide allegation, although it is being closely watched.
Tembeka Ngcukaitobi, a lawyer for the High Court of South Africa, told the ICJ Israel's "genocidal intent" was evident "from the way in which this military attack is being conducted".
"The intent to destroy Gaza has been nurtured at the highest level of state," he said.
"Every day there is mounting, irreparable loss of life, property, dignity and humanity for the Palestinian people," Adila Hassim, also representing South Africa, told the court.
"Nothing will stop the suffering, except an order from this court."
In its evidence submitted before the hearing, South Africa said Israel's actions were "intended to bring about the destruction of a substantial part of the Palestinian national, racial and ethnical group".
Israel will offer its defence on Friday, but has previously said its actions in the Gaza Strip are justified because it is responding to Hamas's deadly attacks on 7 October.
But speaking in court on Thursday, South Africa's Justice Minister Ronald Lamola said that no attack "can provide justification for or defend breaches of the [Genocide] Convention".
Israel is a signatory to the Genocide Convention of 1948, which defines genocide and commits states to prevent it.
On Thursday, Prime Minister Benjamin Netanyahu said "the hypocrisy of South Africa screams to the heavens" - criticising the country for failing to respond to atrocities in Syria and Yemen committed by "partners of Hamas".
"Today we saw an upside-down world. Israel is accused of genocide while it is fighting against genocide," he added.
"Israel is fighting murderous terrorists who carried out crimes against humanity."
The US, meanwhile, said that it saw no justification for South Africa's allegation that Israel has committed genocide.
"They are defending themselves against a still viable threat," said White House national security spokesperson John Kirby.
The ICJ is the United Nation's highest court, based in The Hague in the Netherlands. Its rulings are theoretically legally binding on parties to the ICJ - which include Israel and South Africa - but are not enforceable.
In 2022, the court ordered Russia to "immediately suspend military operations" in Ukraine, an order that was ignored.
Under international law, genocide is defined as committing one or more acts with the intention to destroy, in whole or in part, a national, ethnic, racial or religious group.
There were angry scenes outside the ICJ's building, known as the Peace Palace, as Dutch police struggled to keep groups of Palestinian and Israeli supporters apart.
Hundreds of people waving Palestinian flags gathered outside the ICJ, calling for a ceasefire. Israeli supporters set up a screen showing images of some of the hostages still being held in Gaza.
Red and white police tape has been placed outside the ICJ in an attempt to bring some semblance of order to the chaotic scenes outside.
It was in contrast to the formality inside the court, where the Israeli delegation is listening to South Africa's lawyers accuse the country's forces of committing genocide in Gaza.
Israel's delegation is expected to highlight its right to self-defence under international law - this week, Mr Netanyahu said Israel had no intention of permanently displacing the people of Gaza, or occupying the territory.
Unlike the International Criminal Court (ICC), the ICJ cannot prosecute individuals for crimes such as genocide, but its opinions carry weight with the UN and other international institutions.
On Wednesday, South African President Cyril Ramaphosa said: "Our opposition to the ongoing slaughter of the people of Gaza has driven us as a country to approach the ICJ."
Israeli President Isaac Herzog called the accusations "atrocious and preposterous".
"We will be in the International Court of Justice and we will present proudly our case of using self-defence… under humanitarian law," he said.
He added that the Israeli army was "doing its utmost under extremely complicated circumstances on the ground to make sure that there will be no unintended consequences and no civilian casualties".
The ICJ could rule quickly on South Africa's request for Israel to suspend its military campaign - but a final ruling on whether Israel is committing genocide could take years.
South Africa has been highly critical of Israel's military operation in Gaza, and its governing African National Congress has a long history of solidarity with the Palestinian cause.
It sees parallels with its struggle against apartheid - a policy of racial segregation and discrimination enforced by the white-minority government in South Africa against the country's black majority, until the first democratic elections, in 1994.
In Gaza, more than 23,350 people - mostly women and children - have been killed, according to the Hamas-run health ministry, since the war began in the aftermath of Hamas's 7 October attacks on southern Israel. In those attacks some 1,300 people were killed - mainly civilians - and about 240 others taken hostage.