Israeli leaders have framed an invasion of the southern Gaza city of Rafah as an imperative to achieve its goal of eliminating Hamas. But it’s a strategy that is fraught with complexity and is generating criticism over the potentially catastrophic impact such an operation would have on the more than 1 million Gazans sheltering there.

The planning will likely take Israel’s military some time, Israeli officials and analysts said on Sunday. A major challenge for Israeli forces will be how to move civilians who have crowded into the city out of harm’s way. Many Gazans fled to Rafah on the instructions of the Israeli military to avoid the fighting farther north in Gaza, and a chorus of international leaders have expressed concerns that the people there have nowhere to go.

The prospect of an assault on Rafah is creating tensions with Egypt, which fears a destabilizing influx of Palestinian refugees across its border. Egypt is an important strategic partner for Israel in the region and has played a key role in negotiations aimed at securing the release of Israeli hostages held by Hamas.

The Biden administration has also raised concern over an assault coinciding with the Muslim holy fasting month of Ramadan, according to reports in Israeli media. An attack during Ramadan — which is expected to start March 10, though the timing depends on the sighting of the moon over Mecca — could be viewed as particularly provocative and whip up emotions among Muslims in the region and beyond.

Israeli officials say the military is still working on its plans for invading Rafah and that they have not yet been presented to Prime Minister Benjamin Netanyahu. In the meantime, some have struck a defiant tone about the anticipated assault on a city that officials have called the last Hamas stronghold in Gaza.

“The operation in Rafah will happen,” Avi Dichter, a minister from Mr. Netanyahu’s conservative Likud party, told Israel’s public broadcaster, Kan, on Sunday. “It will begin and it will end, just like in other places,” he said.