Greece's Shipping Ministry issued a "strong recommendation" to Greek shipping companies to avoid waters under Iran's jurisdiction, ministry sources said on Monday.
It was added that this recommendation should be taken into account when sailing in the Persian Gulf, the Strait of Hormuz and the Gulf of Oman.
One of the two Greek ships that were seized last week by Iranian naval forces, 'Prudent Warrior', is anchored at Bandar Abbas, while 'Delta Poseidon', is still in the Persian Gulf.
Two Greeks in the 25-strong crew are onboard 'Delta Poseidon', while 8 Greeks and one Cypriot are onboard 'Prudent Warrior', which has a crew of 23.
All crew members on both ships are in good health, sources noted.
Meanwhile, "Secretary of State Antony J. Blinken spoke today with Greek Foreign Minister Nikos Dendias to condemn in the strongest terms the May 27 seizure of two Greek-flagged vessels by Iran’s Islamic Revolutionary Guard Corps," according to State Department spokesperson Ned Price.
"Iran’s continued harassment of vessels and interference with navigational rights and freedoms are a threat to maritime security and the global economy.
"The Secretary and Foreign Minister agreed that Iran must immediately release the seized vessels, their cargoes, and their crews.
"The United States stands with Greece, our key NATO Ally and partner in the face of this unjustified seizure."
Greek authorities on orders from Washington sparked a diplomatic crisis with Tehran after it seized in April the Russian-flagged Pegas tanker that was carrying Iranian oil.
“Following a request from the US justice system, the oil is to be transferred to the United States at the expense of that country,” a spokeswoman for the Greek port police told AFP, thus confirming 21st century piracy by a supposed modern and law-abiding democracy.
In response to the provocation, Tehran then seized the two Greek vessels.
READ MORE: Turkey threatens NATO says Greek President; Dendias speaks with US over provocations.