Prime Minister Benjamin Netanyahu has said Israel will launch an invasion of the southern Gaza city of Rafah regardless of truce talks with Hamas.
It comes amid ongoing attempts to try to reach an agreement for a ceasefire and hostage releases.
But at a meeting of hostages' relatives, Mr Netanyahu said he would invade "with or without" a deal.
His comments follow renewed warnings by the US against a Rafah invasion unless civilians were properly protected.
In a phone call with Mr Netanyahu on Sunday, US President Joe Biden "reiterated his clear position" on Rafah, a White House statement said. Mr Biden has previously described an invasion of Rafah as a "red line".
More than half of Gaza's 2.5m population is in Rafah, having fled there to escape fighting in other parts of the territory. Conditions in the overcrowded city are dire, with displaced people there have spoken of a lack of food, water and medication.
The West Bank-based Palestinian President Mahmoud Abbas said on Monday that an invasion of Rafah would be the "biggest catastrophe in the Palestinian people's history".
Israeli sources told the Reuters news agency on Monday that plans to attack Rafah would be shelved in favour of a "sustained period of calm" if a ceasefire agreement between Hamas and Israeli was reached.
Days earlier, Israel's foreign minister Israel Katz told Israeli Channel 12 television that "if there will be a deal, we will suspend the [Rafah] operation."
But on Tuesday Mr Netanyahu insisted that the war would continue until Israel had achieved all of its objectives in Rafah.
"The idea that we will halt the war before achieving all of its goals is out of the question," he said.
"We will enter Rafah and we will eliminate the Hamas battalions there with or without a deal, in order to achieve the total victory," according to a statement issued by Mr Netanyahu's office."
It said the families urged the prime minister and his national security adviser, Tzachi Hanegbi, to continue the war and ignore mounting international pressure.
About 130 hostages from among 253 kidnapped by Hamas during its unprecedented attack on Israel on 7 October remain unaccounted for. At least 34 of them are presumed dead. The rest have been released or rescued.
Indirect talks have been at an impasse for weeks, although the US Secretary of State, Antony Blinken, said on Monday that he hoped Hamas would accept what he has called Israel's "extraordinarily offer" for a truce.
Meanwhile the head of the UN's refugee organisation has warned that the looming invasion was causing people in Rafah to live in a state of "constant traumatic stress disorder".
"People have not yet been asked to evacuate from Rafah, but there is a sense that if there is no deal this week that could happen," Philippe Lazzarini told reporters.
"My colleagues on the ground are describing constant state of trauma among the people."