"We try to keep losses at a minimum ... and not be drawn into a war in the mountains."
Meanwhile, Yemeni military officials said they had also engaged in heavy clashes with the Houthi rebels on the outskirts of the northern city of Saada.
A military official told Reuters that Yemeni officials had prevented a rebel attempt to enter the city on Saturday.
The Shia Muslim Houthi fighters, citing political, economic and religious marginalisation, have been battling the government of Ali Abdullah Saleh, the Yemeni president, since 2004.
Saudi Arabia began bombarding suspected Houthi positions earlier this month after they apparently crossed the border and seized control of a small area.
The Houthis say that the Saudis have been allowing Yemeni troops to use the area to attack their positions.
Saudi officials claim that the fighting in northern Yemen is being supported by Iran and could be helping al-Qaeda to cross to their side of the border.