Kingdom says mortar fire from Houthi fighters has killed three army officers and wounded two others in Najran province.
Saudi Arabia has rejected calls by Iran to halt air strikes on neighbouring Yemen, saying Tehran should not interfere in the conflict, now in its second week.
Speaking at a news conference in the Saudi capital Riyadh, Foreign Minister Saud al-Faisal said on Sunday the aerial bombardment on Houthi positions seeks to help a “legitimate” government.
“How can Iran call for us to stop the fighting in Yemen … We came to Yemen to help the legitimate authority, and Iran is not in charge of Yemen,” al-Faisal told a joint news conference with his French counterpart Laurent Fabius.
Saudi Arabia and its Arab allies began air strikes against Iranian-allied Houthi fighters in Yemen on March 26 to try to prevent them from expanding their control across the country.
The Houthis swept into the Yemeni capital Sanaa in September and in February put President Abd-Rabbu Mansour Hadi under house arrest, demanding that he carry out political reforms.
Nine Arab countries, five of them members of the six-nation Gulf Co-operation Council (GCC), are part of the Saudi-led coalition, which is also backed by the United States.
Sunni Saudi Arabia feared the rebels would take over the entire country and move it into the orbit of Shia Iran.
French political support
Fabius, meanwhile, has expressed support for the Saudi-led air strikes against the Houthis.
“Concerning Yemen, we are here to demonstrate our support, especially political, to the Saudi authorities,” he told reporters as he began a series of meetings with the Saudi leadership, including King Salman.
The kingdom is an important ally of France and Fabius reaffirmed to his Saudi hosts that “France is naturally on the side of its regional partners for the restoration of stability in Yemen,” his entourage said.
The Houthis, allied with army units loyal to ex-president Ali Abdullah Saleh, have been battling forces loyal to Hadi, who fled to the Saudi capital Riyadh late last month.
Paris has not so far declared anything other than political support for the Saudi-led coalition and prefers a political solution to the dispute.
“It will be necessary, at one moment or another, to hold talks” for a political solution, Fabius said.
Iran has dismissed as “utter lies” accusations that it has armed the rebels, and its supreme leader Ayatollah Ali Khamenei warned that the coalition’s “criminal acts” against the Houthis must end.