Sarea says this operation was launched due to Saudi Arabia's "blatant aggression" against "our dear people".It reiterates that "maritime navigation is safe for all companies except for Saudi vessels" which it says are "subject to a blockade".
The statement appears to make no mention of Perim Island, in the Bab al-Mandab Strait.
We've just received an expected update from the Houthi's military spokesman.
It doesn't appear to mention the events that have unfolded over the past couple of days - we'll bring you a fuller look at the statement in just a moment.
The Houthis' lightning advance across the southern reaches of the Tihama – Yemen's arid coastal plain – appears to have taken most observers by surprise.
Until recently, the anti-Houthi coalition, known as the National Resistance, held significant territory along Yemen's Red Sea coast. In a matter of days, much of this has fallen to the Houthis, who are enjoying their most significant battlefield gains for years.
But Hisham al-Omeisi, a Washington-based analyst at the European Institute of Peace, says the latest developments are far from surprising.
"The National Resistance forces have been warning… for a while," he tells BBC News, "and unfortunately the international community has been dragging its feet."
"Now that they are there [in Mokha, the Red Sea port city], they're going to be entrenched and it’s going to be a lot more costly to push them out.”
Some see the sudden collapse as an inevitable consequence of a lack of coordination and sporadic infighting among anti-Houthi forces, as well as deep divisions between Saudi Arabia and the United Arab Emirates, who once formed the backbone of the international coalition supporting Yemen's internationally-recognised government.
The latest Houthi advances in Yemen's remote southwest don't just represent a significant development in the course of Yemen's long civil war but also threaten one of the world's most important maritime waterways.
By capturing the small southern port of Mocha and reportedly occupying strategic islands in the southern Red Sea, the Houthis appear to be in a position to control the flow of shipping through the vital Bab al-Mandab strait.
The Iranian-backed rebels, who control much of Yemen's north, including the capital Sanaa, say they will only target Saudi-linked ships, but their record in attacking a wide range of international vessels in response to Israel's war in Gaza will make all nations using the Red Sea extremely nervous.
To the north, satellite images suggesting that Houthi missiles and drones struck Saudi Arabia’s East-West pipeline – a vital alternative route for Saudi oil exports following the closure of the Strait of Hormuz earlier this year – points to an effort by Iran’s Yemeni allies to add to the economic pressures generated by the US-Israeli war with Iran.
With the Strait of Hormuz still mostly closed, the possibility that the Bab al-Mandab might experience a similar fate is a real worry.
BBC Verify has been examining material which shows fighters inside the key Red Sea port city of Mokha yesterday after it was captured by the Houthis.
One verified image shared on Telegram shows four armed men outside the Mohka airport terminal building, which is on the coast, just south of the main sea port.