Saudi Arabia has regained control of territory seized by Yemeni rebels in an incursion last week, a senior official was quoted as saying, as the kingdom becomes more entangled in conflict to its south.
Saudi Arabia launched air strikes on rebels in northern Yemen last week after Shi'ite Muslim insurgents crossed the border into the kingdom and said they had taken control of an area called Jabal Dukhan.
The world's top oil exporter has become increasingly anxious about instability in Yemen, which is facing a Shi'ite insurgency in the north, separatist sentiment in the south and a growing threat from resurgent al Qaeda fighters.
"The situation is calm ... especially in Jabal Dukhan, of which full control has been regained," Prince Khaled bin Sultan bin Abdul-Aziz, assistant minister for defence and aviation, said on Saturday, the Saudi Press Agency (SPA) reported.
Prince Khaled said three members of the Saudi security forces were killed and 15 wounded in fighting on the Saudi-Yemeni border, SPA said.
Four Saudi soldiers were missing, Prince Khaled said, but denied that they had been taken prisoner. He said Saudi security forces had arrested several rebels.
The rebels, referred to as Houthis after the clan of their leader Abdel-Malik al-Houthi, said on Friday they had captured some Saudi soldiers.
In Sanaa, the Yemeni government said one of its fighter planes crashed in a rebel stronghold in the north of the country on Sunday because of a technical fault.
However, the rebels said in an email statement to Reuters that they shot the aircraft down in Saada, a mountainous province in northern Yemen where most of the recent fighting has taken place.
In the past few weeks the Houthis have accused Saudi Arabia of allowing Yemeni forces to use its territory as a base to launch attacks against them and had threatened to respond.
Houthi rebels first took up arms against President Ali Abdullah Saleh's government in 2004, citing political, economic and religious marginalisation by the Saudi- and Western-backed administration.
The conflict intensified in August when Yemen's army launched Operation Scorched Earth.
Aid groups, who have been given limited access to the northern provinces, say up to 150,000 people have fled their homes since 2004.