"I would say the 60-day period officially started today," Vance told reporters at a White House briefing on Thursday.
Asked what happens after the 60-day period in terms of governance of the Strait of Hormuz, Vance repeated the US view that the major supply route for oil and gas shipments should be free of tolls.
Iran largely closed the waterway during the war.
"The final negotiations can set the terms of what comes afterwards," Vance said.
During the 60 days, negotiators are expected to tackle some of the most contentious and unresolved issues that were left open in the initial accord.
These include key questions surrounding Iran's nuclear program and the future of its stockpiles of highly enriched uranium.
Many analysts are sceptical the two sides can forge a final settlement within the 60-day window laid out in the memorandum of understanding.
The 60-day deadline can be extended if both sides agree.
According to Pakistan, which mediated the agreement, the framework accord entered into force with "immediate effect" overnight into Thursday after it was signed by both parties.
Vance said the agreement had already been signed electronically.
"We're going to start the 60-day clock today," he said.
The agreement was initially expected to be formally signed at an in-person ceremony on Friday in Switzerland attended by Vance, with the next stage of talks also kicking off.
Trump subsequently signed a paper copy on Wednesday evening at the Palace of Versailles outside Paris, where French President Emmanuel Macron hosted him following the conclusion of the G7 summit.
Macron, seated beside Trump as he signed the document, told him: "Great job."
Vance, who has taken on the role of Trump's lead negotiator, said he plans to travel to Switzerland for talks with Iran, although the timing has yet to be finalised.
"We're trying to figure out exactly when that's going to happen," he said, adding that the trip could take place as soon as this weekend depending on if arrangements could be made with Iran.
Vance said 12.5 million barrels of crude sailed through the Strait of Hormuz overnight.
Shippers say it will still take time for transit across the strait to reach pre-war levels, with a need to ensure safe access and clear mines.
Lloyd's List editor in chief Richard Meade said for the first time in 110 days, ships owned by major companies were crossing the strait after effectively being marooned there since February.
The strait is a critical passageway for the world's oil and natural gas.
Before the war, the waterway off Iran's coast carried a fifth of the world's crude oil.
Lloyd's List did not say how many ships were transiting through or had passed through the strait as of Thursday.
It said tankers controlled by major ship owners Grimaldi Group, Cosco, Knutsen and NYK had passed through the strait.
with DPA
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