"Its [Saudi Arabia] insistence to continue the aggression after this initiative gives us the legitimacy to open new fronts and to wage an open war," he said.
The so-called Houthi fighters seized an area of Saudi territory in November last year, drawing the kingdom into its long-running conflict with government forces.
Saudi air raids
Since then Saudi Arabia has launched a number of air raids and artillery strikes against the group.
The Houthis say that many of the attacks have taken place inside Yemeni territory and caused many civilian casualties, but Riyadh has repeatedly denied crossing the border with its southern neighbour.
The Saudi army has lost at least 113 soldiers in fighting with the Houthis, Al-Riyadh newspaper quoted General Ali Zaid al-Khawaji, the Saudi southern region commander, as saying.
Al Jazeera's Mohamed Vall, reporting from Sanaa, said that the Houthi's declaration was not a surprise to many people in Yemen.
"But this audio and the initiative they declared did not come across as any kind of agreement between the sides.
"We know that the Houthis have been undergoing severe strikes from the Saudis and could not continue an open ended war against the Saudis, according to many analysts here."
The Houthis, who launched a rebellion against the Yemeni government in 2004, belong to the minority Zaidi sect of Shia Islam and complain of social, economic and religious marginalisation.
Government forces launched "Operation Scorched Earth" on August 11 in an attempt to crush the rebels in the mountainous northern region.
Al-Houthi's announcement on Monday came just three days after he appeared in a video recording denying claims by the Yemeni government that he had been injured or killed.
The rebel leader spoke briefly in the 35-second video posted on the group's website showing him sitting on a chair with no visible injuries.
Saudi Arabia fears that the growing instability in neighbouring Yemen could turn into a major security threat for the kingdom.
The government in Sanaa is battling a secessionist movement in the south and a group calling itself al-Qaeda in the Arabian Peninsula, as well as the Houthi fighters.