Heavy artillery and aircraft pounded the supected position of Houthi fighters inside Yemen, Saudi officials said, creating what the the Saudi media referred to as a "kill zone".
Mohammed Abdel Salam, a spokesman for the Houthis, confirmed to The Associated Press news agency that the Saudi forces were using air raids and artillery strikes to force them back form the border.
"Their goal seems to be establishing a buffer zone or a no man's land on the border," he said.
"It is obvious, they are trying to scare us and make us leave the area."
No ground forces
However, the Saudi government adviser said that there were no Saudi troops fighting on the ground inside Yemen, where the terrain is too mountainous to deploy tanks and artillery effectively.
"The orders are not to go physically into Yemeni territory," he said.
"We don't want to get bogged down there or inflame any local sensitivities, if there are any, against us."
Saudi Arabia launched its offensive against the Houthis, who are named after their deceased former leader, 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.
Prince Khaled bin Sultan, the Saudi deputy defence minister, said the offensive would continue until the Houthis "withdraw dozens of kilometres" from the border.
Riyadh has become increasingly anxious about the stability of the government in Yemen, which is facing opposition from the Shia population in the north, separatist sentiment in the south and a growing threat from al-Qaeda fighters.
The Houthis first took up arms against the government of Ali Abdullah Saleh, Yemen's president, 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 in an attempt to crush the fighters in the northern province of Saada.
Aid groups, which have limited access to the northern provinces, say at least 150,000 people are believed to have fled their homes since 2004.
The United Nations refugee agency said last week it was looking into whether the Saudi air raids had affected 3,500 to 4,500 displaced people gathered near the border.