U.S. and Iranian negotiators held marathon talks in Switzerland into Sunday night as they worked to launch a 60-day effort toward a new nuclear agreement.Why it matters: The nearly nonstop talks at the Lake Lucerne Summit signal both sides remain engaged despite significant differences and may be laying the groundwork for broader discussions on regional security.The talks that Vice President JD Vance is spearheading for the U.S., along with officials including White House envoys Steve Witkoff and Jared Kushner, took place despite Iran claiming on Saturday that it was shutting down the Strait of Hormuz in response to Israeli ceasefire violations in Lebanon.Behind the scenes: The U.S. diplomat said one of the issues during discussions was "deconfliction mechanisms in Lebanon and enforcing the ceasefire," amid clashes between Hezbollah and Israeli troops in the south of the country.Talks focused on "all elements of the nuclear deal." Officials also discussed the Strait of Hormuz and recent Iranian statements about potentially closing it, the diplomat said."We made clear we want to ensure it remains fully open. We made good progress on that front," the U.S. diplomat said.Zoom in: The two sides discussed implementation of the memorandum of understanding and how to ensure all parties are aligned, the diplomat said.Officials also discussed a framework for continuing talks between political leaders and technical teams.Representatives from the U.S., Iran, Pakistan and Qatar appeared pleased with the talks' progress, according to the diplomat."The mediators are helping both sides work through things. We feel this initial round of talks is setting us up for trust building going forward."What's next: High-level political talks are expected to conclude Monday, while technical teams are likely to remain in Switzerland to continue negotiations.