Saudi Arabia says its forces have forced the rebels out of its territory
A commander of the rebels fighting the government in Yemen has called on Saudi Arabia to end its attacks and stressed that his group has no foreign backing.
Abdul Malik al-Houthi told al-Jazeera TV the offensive triggered by a rebel cross-border raid last week was "not in the interest of the two countries".
He also rejected accusations of Iranian help, saying the Houthis had "no links with any foreign political agenda".
Riyadh has said it will hit the rebels until they pull back from its border.
"We have achieved what the supreme commander of the armed forces has ordered us to do, and that's the clearance of every inch of the kingdom," Saudi Deputy Defence Minister Prince Khaled Bin Sultan told troops on Monday.
"Now there is no-one of the Houthis inside the Saudi side of the borders and whoever comes close to it, will be killed."
Earlier, the rebels said Saudi jets had bombed several villages on the Yemeni side of the border, killing two women and wounding a child.
The rebels also said they had taken control of more territory from the Yemeni army elsewhere in the northern province of Saada.
The Houthis, named after the family of their leader, say they are trying to reverse the political, economic and religious marginalisation of the Zaydi Shia community.
They also accuse Saudi Arabia of supporting the Yemeni armed forces by allowing them to launch attacks from its territory, a charge both countries deny.
On Monday evening, Abdul Malik al-Houthi, a field commander, said the war his group was waging was only for self-defence.
"We affirm that whoever tries to add a sectarian dimension to our position is a liar and tries to sow sedition. We respect all the sons of our nation in the Arab region and the entire Muslim world, irrespective of the school of thought or ideology," he said in an audiotape broadcast by al-Jazeera.
"We are not takfiris [who believe contemporary Muslim society has reverted to a state of unbelief and consider rebellion against the state legitimate], nor do we support bloodletting."
"In addition, we do not have any links with any foreign political agenda regarding our position in the current confrontation."
Mr Houthi called on the Saudi government to "stop the aggression, respect the right of neighbourliness, and change its policy, which the Yemeni regime was lured to adopt for the sake of financial goals".
He also warned the Yemeni government that "the escalation of attacks and rejection of dialogue is not in the interest of the two countries".
Earlier, Iran's Foreign Minister, Manouchehr Mottaki, warned against foreign military intervention in the conflict, saying those who took sides would suffer "negative consequences".
The Yemeni government accuses the Houthis of wanting to re-establish Zaydi clerical rule, which ended in 1962.
The Zaydi community are a minority in Yemen, but make up the majority in the north of the country.
The insurgents first took up arms against the government in 2004, after which government forces killed or captured much of the Houthi leadership.
The government launched a fresh offensive in August 2009, which has precipitated a new wave of intense fighting.
Aid agencies say tens of thousands of people have been displaced.