Vice President JD Vance said Thursday that an international security force that has yet to be formed would take the lead on disarming Hamas, which has been one of the thorniest issues when it comes to reaching a lasting peace in Gaza.

The vice president spoke from Israel, at the end of a visit aimed at shoring up a fragile cease-fire between Israel and Hamas. In remarks to reporters, Mr. Vance cautioned that the task of disarming Hamas — which the militant group has long opposed — was “going to take some time and it’s going to depend a lot on the composition of that force.”

The cease-fire deal that came into effect earlier this month was based on a proposal outlined in September by president Trump, which includes a stipulation that a “temporary International Stabilization Force” be deployed in Gaza. But several countries have hesitated to commit troops to such a force because its exact mission in the devastated Palestinian enclave was unclear. The possibility that such a force might be drawn into direct conflict with Hamas fighters has also been a worry.

While Mr. Vance did not address that concern in his brief remarks on Thursday, he reiterated that there would be “no American troops on the ground” in Gaza. Instead, he said, American personnel would be “supervising and mediating the peace.”

The 20-point peace proposal did not specify that the security force would be tasked with disarming Hamas, and a timeline for doing so has not been laid out. The force was originally envisioned as a way to secure areas of Gaza where Israeli troops have withdrawn, prevent munitions from entering the territory, facilitate the distribution of aid and train a Palestinian police force.

The deal has come under strain from a recent flare-up of violence in Gaza, and lingering tensions over the exchange of deceased Israelis and Palestinians.

It faced fresh challenges this week from Israeli lawmakers, who approved a preliminary measure for the annexation of the Israeli-occupied West Bank — a move that is explicitly prohibited under the terms of Mr. Trump’s peace plan.

Mr. Vance said Thursday that the vote was “weird” and leveled sharp criticism at those lawmakers.

“If it was a political stunt, it was a very stupid political stunt, and I personally take some insult to it,” he said. “The West Bank is not going to be annexed by Israel. The policy of the Trump administration is that the West Bank will not be annexed by Israel.”

Mr. Vance also touched on the topic of reconstruction in Gaza, echoing the broad contours of comments made this week in Israel by Jared Kushner, president Trump’s son-in-law, who said efforts to rebuild the enclave could begin in areas still controlled by the Israeli military.

The vice president departed Israel just hours before Secretary of State Marco Rubio arrived in the country. Mr. Rubio met with Prime Minister Benjamin Netanyahu of Israel in Jerusalem on Thursday night.

On Wednesday, Mr. Rubio addressed the proposed creation of an international force. Speaking to reporters at Joint Base Andrews before he flew to Israel, he said that the Trump administration may seek a United Nations “mandate” for the force.

The back-to-back visits by Mr. Vance and Mr. Rubio underscore the administration’s keen interest in preserving the cease-fire. Steve Witkoff, Mr. Trump’s Middle East envoy, and Jared Kushner, the president’s son-in-law, have also been in Israel this week.

Mr. Trump visited the country earlier this month to celebrate the cease-fire agreement.

Several Trump administration officials, speaking on the condition of anonymity to discuss private conversations, have recently said there was concern within the administration that Mr. Netanyahu might vacate the deal.

Before departing for Israel, Mr. Rubio said that American diplomats will soon be assigned to monitor the fragile cease-fire at a new Civil-Military Coordination Center in southern Israel.

“There’s a lot of work to be done,” said Mr. Rubio. “But we certainly wanted to make sure that we were there and ensuring that we had the right people in place at the coordination center, which is key to holding this all together.”

The cease-fire agreement that went into effect earlier this month led to an Israeli military pullback within Gaza, and saw the last 20 Israeli hostages held in the enclave exchanged for almost 2,000 Palestinian prisoners and detainees.