The al Ekhbariya state television showed images of buildings and cars damaged in the attack, which was confirmed by the coalition that has been carrying out air strikes against the Houthi Shia rebels and their allies in Yemen since late March.
Coalition spokesperson Brigadier General Ahmed Assiri told al Ekhbariya that the rebels had "randomly" shelled Najran "hitting hospitals, schools and civilian homes."
"Air and ground forces will respond in the right way to these hazardous acts and will not allow them to be repeated," Assiri said.
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The Saudi military had already deployed Apache combat helicopters to target the rebels in the border area, he added.
The kingdom's ground forces have repeatedly clashed with the rebels near its border with Yemen and its helicopters have been involved in the military action.
Assiri accused the rebels of attempting to sabotage a tentative coalition initiative announced on Monday to pause its air strikes to allow deliveries of humanitarian aid in Yemen.
"After the announcement of the humanitarian initiative yesterday, they want to express their rejection to any peace initiative and so targeted Najran," he said.
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The spokesperson described Tuesday's rebel attacks on Najran as "suicidal", warning that "all those who approach the border will be killed."
The assault on Najran came as Saudi Arabia's King Salman warned at a summit in Riyadh of the threat of Iran to the stability of the region.
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