Iran live updates: Iran's top negotiator says military 'ready to respond' amid Trump threats

Vice President JD Vance said "great progress" was being made in Sunday's U.S.-Iran talks in Switzerland and sought to downplay the Israeli-Hezbollah fighting in Lebanon.

"We've already made great progress over just the last few hours, and I expect it will make additional progress in the hours to come," Vance told reporters in Bürgenstock.

The vice president said many of the U.S.'s goals have already been achieved, and Sunday’s negotiations were about what could be further accomplished through diplomacy.

"The opening of the Strait of Hormuz, the ending of the Iranian nuclear program, all of these things have already been accomplished," Vance said. "The question before us now is how much more can we accomplish together?"

Esmaeil Baqaei, spokesperson for the Iranian foreign ministry, said earlier on Sunday that the "termination of the war on all fronts, including Lebanon" would be among the points discussed. Israel's defense minister also said on Sunday that the Israel Defense Forces did not plan to leave the area they're occupying in southern Lebanon.

Vance continued to minimize the impact of the ongoing conflict in Lebanon on the peace process, again insisting that conditions on the ground have been improving.

"We've seen great progress over the last just a couple of days in ensuring that the ceasefire holds in Lebanon," he said.

-ABC News’ Nicholas Kerr and Hannah Demissie

Israeli Defense Minister Israel Katz said on Sunday that his country's military "will not withdraw from the security zone in Lebanon" and that the Israel Defense Forces are free "to act to eliminate threats."

"Preserving the lives of our soldiers and citizens is a top and absolute priority," Katz added in his statement.

-ABC News' Jordana Miller

Delegations from the United States and Iran arrived on Sunday at the Bürgenstock resort in Switzerland, where talks were set to begin.

Mediators from Pakistan and Qatar have also arrived at the resort, a luxury lakeside retreat outside Lucerne, the Swiss Ministry of Foreign Affairs said on Sunday.

Vice President JD Vance, along with the Trump administration’s envoys, Steve Witkoff and Jared Kushner, met on Sunday with Pakistani officials, including Prime Minister Shehbaz Sharif.

Vance had departed the U.S. on Saturday afternoon. He did not give formal remarks before meeting with Pakistani officials, who have served as key intermediaries for the U.S. in the negotiations. Rather, he thanked the Pakistani delegation for being there and asked how the pool reporters were doing after their flight, noting, "We'll speak to you guys later."

Esmaeil Baqaei, spokesperson for the Iranian foreign ministry, said on Sunday that the talks would focus on key paragraphs in the memorandum of understanding signed by both countries.

He said the "termination of the war on all fronts, including Lebanon," would be among the points discussed.

-ABC News' Rashid Haddou and Nicholas Kerr

Vice President JD Vance landed in Lucerne, Switzerland, just before 12 a.m. ET, according to his office.

No official schedule for his visit has been made public yet.

Vance is set to join Special Envoy Steve Witkoff and Jared Kushner in the region for expected talks with Iran.