The Danish military's Joint Arctic Command (JAC) said Tuesday's tide had failed to lift the 104-meter (341-foot) Ocean Explorer enough to free it.
The US continues to see Iranian harassment of commercial vessels in the Persian Gulf.
According to the ministry, the unregistered yacht was docked at the port with over 100 liters of diesel in the tank.
Russia said its Vasily Bykov patrol ship fired with automatic weapons on the "Sukru Okan" vessel after the captain did not respond to a request to halt for an inspection.
The warning shows tensions remain high in and around the Strait of Hormuz, where Iran seized tankers in late April and early May.
Dubbed Intrinsic Defender, the two-week joint drill is centered on boosting operational readiness and navy-to-navy cooperation.
At the time of the attack, a US RQ-4 Global Hawk unmanned surveillance aircraft was in the central area of the Black Sea, the defense ministry said.
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