Israel's military said it was preparing for "unrelenting attacks" to dismantle Hamas while former US President Barack Obama warned that "any Israeli military strategy that ignores the human costs could ultimately backfire."
The Palestinian health ministry said the Gaza death toll had topped 5000 in two weeks of Israeli air strikes in response to Hamas' 7 October attack on southern Israel in which the Islamist militant group killed more than 1400 people.
Israel pounded hundreds of targets in Gaza from the air on Monday as its soldiers fought Hamas militants during raids into the besieged Palestinian strip where civilians are trapped in harrowing conditions.
Hamas on Monday freed two Israeli women among the more than 200 hostages taken during its 7 October assault. They were the third and fourth hostages to be released.
Israeli Chief of Staff Lieutenant General Herzi Halevi issued a statement suggesting that Israel had no intention of curbing its strikes on the densely populated Gaza Strip and hinting that it was well prepared for a ground assault.
"We want to bring Hamas to a state of full dismantling," Halevi said late Monday. "The path is a path of unrelenting attacks, damaging Hamas everywhere and in every way.
"We are well prepared for the ground operations in the south," he added, referring to southern Israel, which abuts Gaza.
"Troops who have more time are better prepared, and that is what we are doing now."
In public, the United States has stressed Israel's right to defend itself but two sources familiar with the matter said the White House, Pentagon and State Department have stepped up private appeals for caution in conversations with the Israelis.
A US priority is to gain time for negotiations to free other hostages, said the sources, who spoke before the hostage releases were announced on Monday.
Asked about the possibility of a ceasefire, US President Joe Biden said: "We should have those hostages released and then we can talk".
Obama warns Israel against civilian casualties
Obama, in a rare comment by a former US president on a foreign policy crisis, issued a written statement warning Israel not to cause so many civilian casualties in retaliating against Hamas that it would alienate generations of Palestinians.
"Any Israeli military strategy that ignores the human costs could ultimately backfire.
"Already, thousands of Palestinians have been killed in the bombing of Gaza, many of them children. Hundreds of thousands have been forced from their homes," Obama said in a statement posted on social media.
It was not immediately clear whether Obama coordinated his statement with Biden, who was his vice president. The White House did not immediately respond to a request for comment.
"The Israeli government's decision to cut off food, water and electricity to a captive civilian population threatens not only to worsen a growing humanitarian crisis," he added.
"It could further harden Palestinian attitudes for generations, erode global support for Israel, play into the hands of Israel's enemies, and undermine long term efforts to achieve peace and stability in the region," he wrote in the statement published in Medium that also condemned Hamas' attack and reiterated his support for Israel's right to defend itself.
US Secretary of State Antony Blinken planned on Tuesday to attend a UN Security Council meeting on the Middle East, though it was unclear what action, if any, might be taken by the council, whose five veto-wielding powers appear divided.
Israel's bombardment of Gaza has allowed China and Russia to burnish their credentials as the champions of the developing world, in contrast with the United States, which has squarely supported Israel. All three big powers hold Council vetoes.
On Monday, Gaza's health ministry said 436 people had been killed in bombardments over the previous 24 hours, most in the south of the coastal enclave next to which Israeli troops and tanks have massed for a possible ground invasion.
The Israeli military said it had struck more than 320 targets in Gaza over 24 hours, including a tunnel housing Hamas fighters, dozens of command and lookout posts, and mortar and anti-tank missile launcher positions.
The Israeli military said it struck a Hamas target in Gaza's Al-Shati refugee camp that the Palestinian enclave's health ministry said killed or wounded dozens of people late on Monday.
Reuters could not immediately confirm the reports.
At least 5087 Palestinians have been killed in two weeks of strikes, including 2055 children, the health ministry said.
With Gaza's 2.3 million people running short of basics, European leaders looked set to follow the United Nations and Arab nations in calling for a "humanitarian pause" in hostilities so aid could reach them.
A convoy of humanitarian aid trucks delivered water, food and medicine to the Gaza Strip on Monday - the third since aid began flowing on Saturday - but the United Nations said fuel was not included and reserves will run out within two days.
The UN said desperate Gazans also lacked places to shelter from the unrelenting pounding that has flattened swathes of the Hamas-ruled enclave.
- Reuters