The Yemen government has been fighting northern rebels since 2004
Rebels from Yemen have fought their way across the border into Saudi Arabia, where they are now holding out against the military.
The rebels have killed a Saudi officer and injured 11 others, the Saudi authorities confirmed on Wednesday.
The rebels said they had taken "full control" of a mountainous section of the border region of Jabal al-Dukhan.
The Yemen government has been waging a campaign against the Zaidi Shia rebels, also known as Houthis, since 2004.
The Houthis have long accused Riyadh of supporting the Yemeni government in attacks against them.
In October there were clashes between Houthis and Saudi security forces near the border.
Yemen is one of the world's poorest countries and analysts question the ability of the government to assert control over the country.