Two South Korean-operated vessels have exited the Strait of Hormuz following last week's ceasefire agreement between the United States and Iran that reopened the strategic waterway, the maritime ministry said Monday.

Modest reactions in the oil and financial markets as Iran and the U.S. met in Switzerland for a first round of talks aimed at making a temporary cease-fire permanent.

Major shipowners have begun moving vessels through the Strait of Hormuz since the U.S. and Iran signed an interim agreement to end their war, maritime data company Lloyd’s List Intelligence said

Cargo ships and oil tankers are beginning to travel through the strait after the United States and Iran signed an agreement to end the war.

Under the current deal, Iran allows the safe, toll-free passage of commercial ships through the strait for a 60-day period.

The Strait of Hormuz is still operating in a war zone environment, according to Chubb CEO Evan Greenberg. Chubb is insuring ships that pass through the waterway, which normally transits one-fifth of global oil supplies.

The United States and Iranian militaries have offered conflicting accounts over whether the crucial waterway is open.

Sen. Lindsey Graham said on "Face the Nation" June 21 he thinks the U.S. will "obliterate" Iran if the country resists Strait of Hormuz control.

Iran said it has closed the Strait of Hormuz again as Israel and Lebanon continue fighting in spite of the peace plan between the U.S. and Iran.

Fifty-five ships had passed through the strait on Saturday, the U.S. military said. But then Iran’s military said it was closing the waterway once again.