Saudi Arabia’s three-day-old blockade of entry points to Yemen threatens to plunge that war-ravaged country into a famine that could starve millions of people, the top relief official of the United Nations said Wednesday.

The warning by the official, Mark Lowcock, the world body’s coordinator of humanitarian aid, was perhaps the most dire so far regarding the blockade’s effects on what already is one of worst man-made disasters.

Mr. Lowcock spoke at a closed meeting of United Nations Security Council diplomats who have expressed alarm over the deterioration in Yemen, the Arab world’s poorest country.