On Saturday, al-Houthi released an audio message via the internet in which he advised the government not to allow the conflict to be used by "international and regional forces" as an excuse to drag Yemen into a wider war.
"It was these forces and the stupidity of the government that led them to launch attacks on its own people," he said.
"Nevertheless, and for the fourth time, I announce our acceptance of the five conditions [for an end to the conflict] after the aggression stops ... the ball is now in the other party's court."
Al-Houthi did not address the sixth condition, the ending of attacks on Saudi Arabia, which the government in Sanaa added after Riyadh launched an assault against the fighters in November.
"This is a key demand we cannot make concessions on," Tarek al-Shami, a spokesman for Yemen's ruling party, said on Sunday.
And Mohammed Qubaty, a member of Yemen's ruling party, said al-Houthi's offer was ambigious.
"From one side, they ignore one of the six conditions ... from the other, he makes no reference to implementation of the other five conditions," he said.
"They say they accept them, but want to start a dialogue about implementing them, while the government wants them to get on with implementation immediately.
"I think the rebels are cornered now and are trying to buy time."
A Saudi military source told Reuters news agency that Houthi snipers were still crossing the border into Saudi territory and exchanging fire with Saudi troops, nearly a week after the rebels said they would withdraw from Saudi territory.
Al-Houthi had announced on January 25 that his fighters were pulling out of Saudi Arabia, but with the warning that "if the Saudi regime maintains its aggression after this initiative, it would be showing that its intention is not to defend its territory, but to invade our borders".
The Saudi government said it was they who had driven the rebels out of the border region.
"They did not withdraw. They were forced out," Prince Khalid bin Sultan, the Saudi deputy defence minister, said.
And in order for Saudi Arabia to accept the Houthi ceasefire, Sultan said the rebels must create a 10km buffer zone between them and the border, agree to let Yemen's military to take up positions along it, and return six captured Saudi soldiers.
The Houthis have been engaged in sporadic fighting with government forces since 2004, in a war they say is to defend their community against discrimination and the aggression of local government representatives in the northern Saada province.
The latest stage of the conflict broke out on August 11, when the military launched Operation Scorched Earth - an all-out assault against the rebels.
According to international aid organisations, more than 200,000 people have been displaced by the fighting since 2004.