Saleh's statement came on a day heavy clashes were reported at the Saudi-Yemeni border between Saudi government forces and Houthi fighters for the fifth straight day.
Saudi Arabia, which the Houthis accuse of providing support to Yemen's military, has become increasingly concerned about the violence along its southern border since it flared up in August.
There have been claims that Iran, the predominantly Shia rival of Sunni Saudi Arabia for power in the region, has been providing assistance to the Houthis.
Saudi commanders said troops were shelling suspected Houthi positions.
Smoke could be seen rising above the Jebel al-Dukhan peak that marks the frontier, near the border town of Khubah.
A medical official said seven Saudis, four of them female civilians, had been killed and 126 people wounded since the fighting erupted on Tuesday.
The Houthis claimed on Friday to have captured some Saudi soldiers.
Mohammed Abdel-Salam, a spokesman for the Houthis, told Al Jazeera that the men were seized after Saudi ground forces crossed into Yemeni territory.
Abdel-Salam said the captured soldiers would be interviewed but "will be treated with respect".
Prince Khaled bin Sultan bin Abdul-Aziz, Saudi Arabia's assistant minister for defence and aviation, said four Saudi soldiers were missing, but denied that they had been taken prisoner.
Abdel-Salam demanded an end to the "unjust Saudi aggression" and said Riyadh should stop Yemeni forces from using what he called bases inside Saudi territory to attack the Houthis.
Saudi Arabia insists its operations against the fighters have been limited to air raids and artillery strikes.
Houthi fighters have tried to prove that Saudi troops had crossed over the border by releasing video footage purportedly showing the Saudi military in Yemeni territory.
Mohammed al-Qadhi, a foreign correspondent for The National newspaper of Abu Dhabi, said the Saudi military was already deeply involved in the conflict.
"According to some sources in Saada, there is fierce fighting between the Saudi army and the Houthis at the border," he said.
"The rebels, who have been fighting an intermittent war for five years, are sending a clear message to show that they are not a group just fighting the government, but they are a regional player just like Hezbollah."
Khalid al-Dakhil, a political analyst at the King Saud University, said that it is impossible for Riyadh to ignore the conflict between the Houthis and the Yemeni government.
|The Houthis have released video footage to prove their claim of Saudi cross-border raids
"The Houthis seem to be very determined in pinning down the Yemeni army, and the Saudi government cannot afford to just sit [idly] by and watch what is happening. They have to support the Yemeni government", he told Al Jazeera.
"The co-operation between Yemen and Saudi Arabia runs for a long time now, even before the Houthis.
"I don't think the Houthis have any chance of succeeding in the end. They will be isolated, they will be squeezed between two armies and I think eventually they will run out of any luck."
Hundreds of people have died in northern Yemen since the country's army began its offensive against the Houthis on August 11.
The fighters, concentrated mainly in the Saada and Amran provinces, are known as Houthis after their late leader, Abdul-Malik's brother Hussein Badr Eddin al-Houthi, a Zaidi leader who was killed by the Yemeni army in September 2004.
An offshoot of Shia Islam, the Zaidis are a minority in a predominantly Sunni Arabian peninsula but form the majority in northern Yemen. Only a small minority of Zaidis are involved in the Houthi uprising.
The Yemeni government accuses the Houthis of seeking to restore an imamate overthrown in a 1962 coup that sparked eight years of civil war.
The Houthis insist they are fighting to defend their community against government aggression and marginalisation.
The Yemeni government said on October 28 that it had arrested five Iranians on a boat loaded with weapons allegedly destined for the Houthis.
But the group denies receiving any help from Tehran, which has offered to mediate in the conflict.
Abdul-Malik al-Houthi, the Houthis' leader, told Al Jazeera that there was no way for Iran to get weapons to his men in the far north of Yemen. "Weapons are largely available in Yemen," he said.
He said his fighters had also seized arms from the Yemeni army, including those taken from captured security posts.
Al-Houthi said his group had no ambitions to target territory in Saudi Arabia. "Saudi Arabia has always co-operated with Yemen, but this co-operation has now taken a new shape," he said.