A Saudi border post in the kingdom's southern region of Jazan came under shell and rocket fire from Yemeni territory yesterday.
After initially reporting that one soldier had been killed in the attack, an interior ministry spokesman said today that two others had succumbed to their wounds.
Quoted by the official SPA news agency, the spokesman did not give a number of those thought to have been wounded in the attack.
In a separate incident, a Saudi soldier operating along the border with Yemen was killed when his vehicle overturned, the spokesman added.
Riyadh said Sunday that rocket fire had killed a general, the highest-ranking officer to die in cross-border attacks since a Saudi-led coalition began air strikes against Iran-backed rebels across Yemen in March.
Nearly 60 people, mainly military personnel, have been killed in Saudi Arabia's border region since the air campaign began.