Germany, a key European ally, announced it would halt exports of military equipment to Israel that could be used in Gaza.
Britain urged Israel to reconsider its decision to escalate the Gaza military campaign.
However, US President Donald Trump's ambassador to Israel, Mike Huckabee, told Reuters that some countries appeared to be putting pressure on Israel rather than on the militant group Hamas, whose deadly attack on Israel in 2023 ignited the war.
In Israel, families of hostages held by militants in Gaza, and opposition leaders blasted Prime Minister Benjamin Netanyahu for a decision that they said would put hostages' lives at risk.
Far-right allies in Netanyahu's coalition have been pushing for a total takeover of Gaza as part of his vow to eradicate Hamas militants, though the military has warned this could endanger the lives of remaining hostages held by militants.
Opposition leader Yair Lapid called the decision to send Israeli forces into Gaza City a disaster, saying it defied the advice of military and security officials.
Netanyahu told Fox News that the military intended to take control of all of Gaza.
The announcement from the prime minister's office early on Friday after Thursday's security cabinet meeting said the military would take Gaza City, but did not say if Israeli forces would take all of the enclave.
Israel's cabinet is expected to endorse the Gaza City plan.
The military has said that it controls around 75 per cent of Gaza. Amir Avivi, a retired Israeli brigadier general, estimated that if the military did take Gaza City, it would give Israel control of about 85 per cent of the strip.
"Gaza City is the heart of Gaza. It's really the centre of government. It has always been the strongest and even in the eyes of Hamas, the fall of Gaza City is pretty much the fall of Hamas," said Avivi.
"Taking over Gaza City is a game changer."
European Commission President Ursula von der Leyen was among foreign leaders urging Israel to reconsider its decision to advance into Gaza City.
Regional power Saudi Arabia, which has said it could not normalise ties with Israel without the establishment of a Palestinian state, condemned any move to occupy Gaza.
In recent weeks, Britain, Canada and France said they could recognise a Palestinian state at the UN General Assembly next month.
The Hostages Families Forum, which represents many families of captives in Gaza, said the pursuit of occupying Gaza means abandoning the hostages, all while ignoring public support to immediately end the war in a deal that releases the hostages.
It said in a statement that the security cabinet had chosen to "embark on another march of recklessness, on the backs of the hostages, the soldiers, and Israeli society as a whole".
"I think it's a death sentence to all the hostages that are still being held there. And it's the wrong decision to do it at this time," Danny Bukovsky, a hotelier in Tel Aviv, said of the announcement that Israeli forces would move into Gaza City.
