Three Saudi troops and “dozens” of Houthi rebels were killed as Saudi forces repelled a major attack from inside Yemen, Saudi officials say.
The rebels attacked near the town of Najran, reports say, in what would be their biggest assault on Saudi soil since a Saudi military campaign began.
A Saudi-led coalition has staged air strikes against rebels since late March in support of Yemen’s exiled president.
Meanwhile aid groups say a lack of fuel is threatening their operations there.
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A statement by the Saudi Press Agency, SPA, said the overnight attack happened on its southern border.
Identifying the attackers as Shia Houthi rebels and groups allied to them, SPA said Saudi ground troops exchanged fire with them and called in air strikes.
The rebels – who control much of northern Yemen, including the capital Sanaa – have been fighting forces linked to the government for several months.
Saudi Arabia and other Arab states have been carrying out air strikes over the last month, with the declared aim of restoring exiled President Abdrabbuh Mansour Hadi.
Earlier on Thursday, a Saudi border guard was killed by a mortar shell close to the border with Yemen in the south-west Saudi province of Jizan. Seventeen Saudi troops have been killed in attacks by Yemeni rebels during the last five weeks.
Meanwhile, UN Secretary General Ban Ki-moon said that he was gravely concerned about the “continued ground fighting and aerial bombardment in Yemen and its impact on innocent civilians”.
More than 1,200 people have been killed and 300,000 have fled their homes in the past six weeks, according to the UN.
“There are credible reports of families in Aden trapped by the bombardment and snipers targeting civilians in the street,” a statement from Mr Ban said.
He called for an immediate ceasefire and urged all parties to ensure that humanitarian agencies have safe and reliable access.
On Thursday, the UN’s World Food Programme (WFP) said it had been forced to withdraw from the western Hudaydah province after running out of fuel there – and that it may have to pull out of other areas soon.
The warning was echoed by the International Committee for the Red Cross, that said a lack of fuel – as well as restrictions on imports – meant hospitals were struggling to provide an adequate level of care.
Purnima Kashyap, the WFP’s country director in Yemen, said: “This is a country where half the population are considered food-insecure, meaning that many families do not know where their next meal will come from.”