As international diplomats converged in the Middle East on Sunday seeking a cease-fire in the Gaza Strip, Israel wrestled with whether to go forward with a ground invasion of Rafah, Hamas’s last bastion in the enclave, according to Israeli officials and analysts.

Israeli officials have said repeatedly that they plan to move into Rafah, but over the weekend, they made clear they were open to holding off if it meant they could secure the release of Israeli hostages taken when Hamas attacked Israel on Oct. 7.

Benny Gantz, a member of the Israeli war cabinet, said Sunday that while “entering Rafah is important for the long battle against Hamas,” freeing the remaining hostages, whose number is estimated at about 100, “is urgent and much more important.”

As Secretary of State Antony J. Blinken headed for Saudi Arabia on Sunday to meet with officials from a half-dozen Arab nations, an American official said Mr. Blinken’s top priority was a cease-fire deal that would include the release of all hostages.

“It would allow for all those hostages to get out,” John Kirby, the U.S. national security spokesman, said on the ABC News program “This Week.” “And to, of course, allow for easier aid access in places in Gaza, particularly in the north. So he’s going to be working at that very, very hard.”

Israel has been under intense international pressure — including from the United States — not to invade Rafah, in Gaza’s south, where more than a million Palestinians have fled the war and are already living in dire conditions.

On Sunday, that pressure appeared to be growing.

Israeli officials increasingly believe that the International Criminal Court is preparing to issue arrest warrants for senior government officials on charges related to the conflict with Hamas, according to five Israeli and foreign officials. The Israeli and foreign officials also believe the court is weighing arrest warrants for leaders from Hamas.

On Sunday, hours after Mr. Blinken left on his trip, President Biden spoke again with Benjamin Netanyahu, the Israeli prime minister, about the cease-fire talks. “The leaders discussed Rafah, and the president reiterated his clear position,” the White House said in a statement about the phone call.

The call came three weeks after Mr. Biden told Mr. Netanyahu that he would rethink American support for the military campaign in Gaza if Israel did not do more to limit civilian casualties and improve the flow of desperately needed food and other supplies into the battered enclave. Humanitarian aid to Gaza has increased substantially since then, although U.S. officials acknowledge that much more is needed.

The Israeli military has already started calling up reserve soldiers for a potential Rafah operation, and an Israeli official said its military could start evacuating civilians by the end of the month. But the official said that an evacuation could take weeks, and that Israel was also using the threat of an imminent military maneuver to press Hamas into a hostage deal.

Another Israeli official said the government was conveying the message that Israel would not wait much longer for an agreement and that if Hamas wanted to stave off an assault on Rafah, it needed to release hostages. Both officials spoke on the condition of anonymity to discuss confidential matters.

In recent weeks, as the death toll in Gaza has climbed, negotiations on a cease-fire have appeared stalled. About 1,200 people were killed in the Hamas-led attack on Israel in October. Health officials in Gaza now put the death toll there at more than 34,000.

On his trip to the Middle East, Mr. Blinken is expected to meet with, among others, officials from Egypt and Qatar. Those countries have served as intermediaries with Hamas in the cease-fire and hostage talks. Mr. Blinken will attend a three-day meeting of the World Economic Forum, and possibly meet with Crown Prince Mohammed bin Salman to discuss the war. He is then planning to travel to Jordan and Israel.

Egypt — which is particularly concerned about an invasion of Rafah since the city borders its territory — has been consulting with Israel and is pushing a proposal for a two-phase hostage deal, one of the Israeli officials said on Sunday.

That proposal, according to the Israeli official, involves an initial “humanitarian” deal for Hamas to release the most vulnerable hostages — women, children, the physically and mentally ill and the elderly — in return for a temporary cease-fire and the release of Palestinian prisoners held by Israel.

After that initial phase, the official said, negotiations could begin for a second phase in which all remaining hostages would be returned in exchange for an end to the war.

There was no immediate comment from Hamas, Qatar or Egypt about the proposal’s details. But Hamas and the Qatari mediators appear increasingly to be trying to engage the Israeli public directly, perhaps to increase pressure on the government for a deal.

In recent days, Hamas released two propaganda videos featuring three of the hostages. And in rare interviews this weekend with two Israeli news media outlets, a spokesman for Qatar’s foreign ministry blamed both Israel and Hamas for the months of deadlock in the talks.

“We were hoping to see much more flexibility,” the spokesman, Majed al-Ansari, told Haaretz, “much more seriousness, much more commitment on both sides, all through the process, from Day 1.”

For Israel, analysts say, the Rafah calculus is complicated.

“Without going into Rafah, it seems like nothing has been accomplished,” said Nachman Shai, a former Israeli government minister and military spokesman.

After six months of war, Hamas’s leadership is still mostly intact, he said, even if the majority of its battalions have been dismantled or degraded.

A ground invasion of Rafah could have unpredictable results, however. It might pressure the Hamas leaders believed to be hiding there into releasing hostages, but it might also lead them to call off any deal, Mr. Shai said.

Reporting was contributed by Peter Baker, Vivek Shankar and Aurelien Breeden.