Saudi Arabia said three of its soldiers and "dozens" of Yemen's Shiite rebels were killed in overnight clashes after the rebels carried out a cross border attack.

The attack late Thursday was the first major incursion into Saudi Arabia by the Yemeni rebels, known as Houthis, since a Saudi-led coalition of mostly Sunni Arab nations began carrying out airstrikes inside Yemen more than a month ago. The kingdom's Defense Ministry did not say how far into the area of Najran the rebels advanced.

The Saudi-led offensive in Yemen aims to diminish the military and fighting capabilities of the Iran-allied Shiite rebels, who have overrun the capital, Sanaa, and are advancing deep into southern Yemen.

The Shiite rebels, whose stronghold is in Saada in northern Yemen, are allied with Yemeni military and security forces loyal to ousted President Ali Abdullah Saleh.

Overnight Saudi airstrikes in Sanaa targeted the positions of the rebels and allied forces, killing at least 14 civilians, including 10 women and children, officials and witnesses said Friday.

One airstrike targeted a house of a top Houthi rebel commander in a Sanaa district called Saawan, demolishing at least six houses, security officials and eyewitnesses told an Associated Press reporter at the scene.

Along the Saudi border, a group of Houthi fighters attacked "border posts and control points" in the southern Saudi region of Najran Thursday night, the kingdom's Defense Ministry said. Saudi forces, backed by fighter jets, repelled the attack, the statement said.

"Dozens of the militiamen were killed. Three soldiers of the ground troops were martyred," according to the statement.

At least 11 Saudi soldiers have been killed in similar border clashes with the Houthis since the kingdom launched airstrikes against the rebels inside Yemen on March 26.

The kingdom's security forces said on April 11 that more than 500 Houthi rebels have been killed in border clashes, with most taking place along the area of Najran. The kingdom has offered the families of each slain soldier 1 million Saudi riyals, or about $267,000, to compensate for their loss.

Saudi Arabia boosted its troop numbers along the roughly 800 mile long border with Yemen since the airstrikes began. The forces frequently fire at suspected rebel positions with both cannon and mortar fire.

The area across the border is considered a Houthi stronghold and its fighters managed to take over several scattered Saudi villages in the southern border region of Jizan in 2009, during the kingdom's last war with the rebels.

Jizan is about 125 miles east of Najran and about 10,000 tribesmen from Jizan have volunteered with their own weapons to stand at the border alongside the Saudi soldiers, commanders in the area say.

Last week during an AP trip to military positions in Jizan and Najran, the commander of forces in Najran, Brig. Gen. Abdullah al-Shehri, said the border situation was stable. The war has so far not included a ground force operation in Yemen but al-Shehri said his forces were prepared for any eventuality.

The war has pushed Yemen further into chaos.

On Thursday, U.N. Secretary General Ban Ki-moon said more than 1,200 people have been killed and that the country's health, water, and telecommunications system are "on the brink of collapse." Ban appealed for an immediate ceasefire, or at least humanitarian pauses.

Yemen's Western-backed president, Abed Rabbo Mansour Hadi, fled the capital earlier this year after being placed under house arrest by the rebels. Hadi temporarily set up a provisional capital in the southern port city of Aden, but later fled the country to Saudi Arabia as the rebels forces advanced on Aden.

Despite more than a month of airstrikes, the campaign has largely failed to halt the rebel advance into southern Yemen.

However, the Saudi government says its coalition campaign has eliminated much of the threat posed to its security by destroying stockpiles of missiles and heavy weapons that were allegedly under the control of Saleh's forces and his rebel allies. The kingdom says it also succeeded in barring Iran from delivering more money and weapons to the Houthis.

Iran and the Houthis deny that Tehran has ever armed the rebels, but acknowledge humanitarian and political support from the Shiite nation.