"Securing navigation in the Red Sea and protecting Bab al-Mandab Strait is a top priority for Egypt's national security," Abdel Fattah al-Sisi said in a statement.
The Red Sea is at the southern end of the Suez Canal, through which much of the world's maritime trade passes.
Later, in a speech broadcast on state television, Sisi said securing the key waterway was also a matter of "Arab national security".
A Saudi-led coalition of more than 10 countries, including Egypt, launched an offensive against Yemen's Huthi rebels on March 26 after the Shiite militia advanced to the southern province of Aden.
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Egypt is taking part in the campaign with its air force and navy, and has pledged to commit ground troops if needed.
Yemen's main southern city of Aden, a last foothold of supporters of self-exiled President Abedrabbo Mansour Hadi, has been shaken by more than a week of fierce clashes between Shiite rebels and loyalist militia.
The strait, only 32 kilometres (20 miles) wide, separates southwestern Yemen from the small African country of Djibouti. Control of it by a hostile power could severely threaten maritime traffic passing between the Mediterranean Sea and the Indian Ocean.