Prime Minister Benjamin Netanyahu of Israel, brushing aside a chorus of international condemnation, said Sunday that an invasion of the southern Gazan city of Rafah would move forward as soon as Israel completed plans for the more than a million people sheltering there to be allowed to move to safety.

“Those who say that under no circumstances should we enter Rafah are basically saying: ‘Lose the war,’” Mr. Netanyahu said on This Week With George Stephanopoulos.

But given the complexity of an operation in Rafah, a ground invasion does not appear likely to happen any time soon, analysts said. More than half of Gaza’s 2.2 million residents fled there to avoid fighting farther north, packing the city with refugees with nowhere else to go.

One Hamas official, Basem Naim, said Mr. Netanyahu was “deluding himself” if he thought that threatening to invade Rafah would increase the pressure on Palestinian negotiators to agree to Israel’s terms for a cease-fire. More than 28,000 people in Gaza, many of them women and children, have already been killed since the war began in October, Gazan health officials say.

“Such an invasion would mean more massacres and intensify the humanitarian disaster,” Mr. Naim said in a text message on Sunday.

Yaakov Amidror, a retired Israeli general and national security adviser, said that while Israel “must go into Rafah” to achieve its objectives of dismantling Hamas’s military capabilities and its ability to rule the Gaza Strip, the invasion would take time to plan.

“It is not imminent,” said Mr. Amidror, now a fellow at the Jerusalem Institute for Strategic Studies, a conservative think tank, “but it will have to be done.”

Mr. Netanyahu insisted that Israel is serious about protecting civilians. “We’re not cavalier about this,” Mr. Netanyahu said. “This is part of our war effort, to get civilians out of harm’s way.”

In a telephone conversation on Sunday, President Biden told the Israeli prime minister that a military operation in Rafah should precede only with “a credible and executable plan” for ensuring the safety of the people taking shelter there, according to the White House.

For weeks, Israel has been discussing plans to send troops to Rafah, where it had directed Palestinians to go for safety, despite a growing demand from world leaders that it agree to a cease-fire. Mr. Netanyahu has publicly rejected Hamas’s latest offer for a pause in fighting that would open the way for the release of the hostages seized when Hamas-led raiders attacked Israel on Oct. 7, killing, Israeli officials say, about 1,200 people.

But the Netanyahu government has signaled that it is still open to negotiations, and the Biden administration has said they will continue in the days ahead.

Rafah sits along the border with Egypt, which has refused to take in Palestinian refugees, fearful for its own security and worried that a displacement could become permanent and undermine Palestinian aspirations for statehood. Egypt has reinforced its frontier with Gaza and also warned Israel that any move that sent Gazans spilling into its territory could jeopardize the Israel-Egypt peace treaty, an anchor of Middle East stability since 1979.

The Biden administration has raised concerns at the prospect of fighting taking place during the Muslim holy fasting month of Ramadan, according to two Israeli officials with knowledge of the discussions. An attack during Ramadan — which is timed to the lunar calendar and expected to start on March 10 — could be viewed as particularly provocative to Muslims in the region and beyond.

Avi Dichter, a minister from Mr. Netanyahu’s conservative Likud party, dismissed concerns about the timing. “Ramadan is not a month without wars,” he told Israel’s public broadcaster, Kan, on Sunday, noting that Egypt went to war against Israel in 1973 during Ramadan. “It never was.”

In Rafah, where many refugees are exhausted after having already been displaced multiple times, some were anxiously trying to figure out their next move. Rafah was the fifth place one Palestinian, Ghada al-Kurd, had fled to with her sister, brother-in-law and four nieces and nephews since they left their homes in Gaza City in October, Ms. al-Kurd said by telephone on Sunday.

“I regret leaving Gaza City,” said Ms. al-Kurd, 37.

She said she had not seen her two daughters in nearly four months because they stayed behind in the north with their father. “If I stayed home,” she said, “it would have been better than all the suffering and humiliation of displacement, because every time you flee to a new place you have to start all over again.”

Mohammed al-Baradie, 24, was preparing to move again from his tent in Rafah under the “constant threat from the Israeli Army to invade Rafah city,” he said in a WhatsApp message on Saturday. Mr. al-Baradie had already moved three times since his home in Gaza City was bombed at the beginning of the war.

“We are so tired,” Mr. al-Baradie said in a voice message.

Reporting was contributed by Hiba Yazbek, Aaron Boxerman, Emma Bubola and Gabby Sobelman.