Saudi Arabia said Friday it carried out airstrikes against "infiltrators" from Yemen that were limited to areas inside Saudi territory, and vowed to press on with the military action until the border with its restive neighbor was secure.

The statement, carried by the official Saudi Press Agency, did not identify the infiltrators or address claims by Arab diplomats on Thursday that the strikes hit across the boundary, targeting Shiite rebels who have been battling Yemeni government forces for the past few months in Yemen's northern Saada province.

The SPA statement stressed the Saudi military action was confined to areas within the kingdom's borders.

In Yemen, however, a military official said Saudi forces on Friday continued to shell rebel position in Saada. He spoke on condition of anonymity because he wasn't authorized to speak to the media.

But regardless of the location of the impact, the offensive threatens to embroil Riyadh in a conflict that has for months been a major source of worry for the oil-rich kingdom.

Riyadh has been concerned about a spillover of the Yemeni fighting, of Iran's alleged involvement in the conflict, and of the possibility that Yemen-based al-Qaida militants could capitalize on the tense situation by smuggling fighters across the long and difficult-to-control border.

More broadly, it raises concerns of another proxy war in the Middle East between Iran and Saudi Arabia, a key U.S. ally.

The Yemeni government has accused Shiite Iran of aiding the rebels while the rebels have accused Sunni Saudi Arabia, Iran's fiercest regional rival, of carrying out bombing runs against them.

The same dynamic has played out in various forms in Lebanon, where Iran supports the Shiite militant Hezbollah and Saudi Arabia favors a U.S.-backed faction, and in Iraq, where Saudi Arabia and Iran have thrown support to conflicting sides in the Sunni-Shiite fault-line.

The Arab diplomats and Yemeni rebels said Saudi fighter jets and artillery bombardments hit across the border into northern Yemen on Thursday — the first reported Saudi incursion into Yemen in years.

The northern rebels, known as Hawthis, have been battling Yemeni government forces the past few months in the latest flare-up of a sporadic five-year conflict. They claim their needs are ignored by a Yemeni government that is increasingly allied with hard-line Sunni fundamentalists, who consider Shiites heretics.

The rebels said the Saudi airstrikes hit five areas in their northern stronghold but it was not possible to independently verify the reports. They said there were dead and wounded, and that homes were destroyed. The rebels' spokesman said people were afraid to get near the areas being bombed, making it difficult to count the casualties.

The SPA statement quoted an unidentified Saudi official as saying the Saudi offensive was prompted by an attack by infiltrators from Yemen who on Tuesday attacked Saudi border guards in the Mount Dokhan area, killing one Saudi soldier and wounding eleven.

The Saudi official said that attack and the infiltrator's presence on Saudi soil were a violation of Saudi sovereignty.

"That gives the kingdom the full right to take all measures to put an end to this illegal presence," the statement said. "The operations will continue until all positions inside Saudi territory are purged of all hostile elements. All necessary measures will be taken to prevent this from happening again in the future."

The statement said that since Tuesday's ambush, the Saudi military has carried out concentrated airstrikes against the gunmen in the Mount Dokhan region and other areas within Saudi borders.

The military also beefed up border security, "silenced the origin of the infiltrators' fire," tightened control over the areas where the infiltrators had tried to establish a presence and evacuated border villages.

The weak central government of Yemen, which has little control outside the capital San'a, is fighting on multiple fronts including the northern rebels and a separatist movement in the south. But the most worrisome is a lingering threat from al-Qaida militants in this impoverished country on the tip of the Arabian Peninsula.

Yemen, the ancestral homeland of Osama bin Laden, has cooperated with the U.S. in fighting terrorism but has struggled to confront Islamic extremists. Al-Qaida claimed responsibility for an attack that killed three senior Yemeni security officers on Tuesday, when gunmen ambushed a government motorcade in a southern province.