"It is not about Iran," Miller said at a news conference in the Bahraini capital Manama, the fleet's headquarters, saying the manoeuvres were "purely defensive".
Iran on Tuesday warned against any "provocations" in the Gulf as the US-led international naval force began preparing for the exercise.
"Our message does not get to one country... It is about a secure maritime environment," Miller said.
"It is purely defensive, not provocative, and takes place in international waters."
Miller said that "critical to the global economy... Is a maritime environment that has free-flowing commerce, ships can safely sail."
"If some nation puts mines into the waters then the global community has to get them from the waters as quickly as possible," he said, adding that the "newest technologies" will be used in the manoeuvres.
Thirty-five ships, 18 Unmanned Underwater Vehicles and more than 100 explosive ordinance disposal divers will participate in the anti-mine manoeuvres running until the end of May.
Iran's Fars news agency reported earlier this week that a minesweeping exercise was being conducted by Iranian forces in the east of the strategic Strait of Hormuz.
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