One US official, speaking on condition of anonymity, told Reuters the exercises involved at least 100 vessels and possibly more, including small boats.
The US military's Central Command confirmed to Reuters that it has seen an increase in Iranian activity, including in the Strait of Hormuz, a strategic waterway for oil shipments that Iran's Revolutionary Guards have threatened to block. Officials at the Pentagon said they expected the exercise would last only a few hours, although it was unclear Thursday night whether it had ended.
They have also expressed concern about keeping open the waterways off Yemen, where rebels backed by Iran have attacked oil tankers.
The exercises come at a time of increased tension between Iran and the United States, which has pulled out of a historic nuclear pact and is slapping fresh sanctions on Tehran on Monday.
The Strait of Hormuz links the Persian Gulf to the Arabian Sea.
But one week later, during a joint press conference with the Italian Prime Minister, Trump said he was willing to meet with Iranian leaders with no preconditions.
Other sources said the Navy's 5th Fleet, which operates American assets around the Gulf, was weighing potential retaliatory moves to Iran's exercise.
Should Iran try to cut off the free-trade route, Richardson said, the U.S. Navy and its allies operating in the region will "be able to handle that threat".
The historic nuclear deal from 2015 provides for the removal of sanctions against Iran in exchange for limiting its opportunities for the enrichment and storage of nuclear materials.
Nevertheless, these Iranian threats are most likely a bluff.
"If any oil faucet in the region is turned on and the petrodollars go to the pocket of those who threaten Iran, it will definitely have impacts on the security of the strait", he said, according to the state-controlled Fars News Agency.
The Strait of Hormuz hosts about 20 percent of the global trade in oil and choking it off would add to supply-side strains that would come in November if USA sanctions manage to isolate Iranian oil from the market.
Senior Iranian officials have warned that they will fight the US efforts to cut off the country's oil exports.
Last week, Defense Secretary Jim Mattis warned Iran that shutting down the Strait of Hormuz would be considered an attack on global shipping.