Container shipping group Hapag-Lloyd said on Friday that one of its ships has crossed the Strait of Hormuz but did not have any information on the circumstances or timing.
Four out of initially six ships remain in the Persian Gulf, after one ship's charter agreement expired, meaning it no longer belongs to the Hapag-Lloyd fleet, a spokesperson added.
The four Hapag ships remaining in the gulf are staffed with 100 crew, who are well-supplied with food and water, he said.
Scores of tankers and other vessels remain stuck in the gulf as the United States is struggling to keep control of the Strait of Hormuz, one of the world's busiest shipping corridors.
The Iran war, launched by the US and Israel on February 28, has been paused since a ceasefire on April 8.
The US and Iran met in Pakistan in an attempt to end hostilities, but talks ended without agreement and a second round has yet to take place.
Tehran says it will not consider opening the strait until the US lifts its blockade of Iran's shipping, which Washington imposed during the ceasefire and Tehran calls a violation of that truce.
This week, Iran flaunted its grip over the strait with a video of commandos in a speedboat storming a huge cargo ship.
(Reporting by Elke Ahlswede, writing by Thomas Seythal, editing by Miranda Murray)