On January 1, Yemen's Higher Security Committee issued conditions for a full ceasefire.
They included the re-establishment of safe passage on roads, the surrender of mountain strongholds, a full withdrawal from all local authority property, the return of all military and public equipment seized during hostilities and the release of all the detained civilians and soldiers.
But Mohamed Vall, Al Jazeera's correspondent in Yemen, reported that Saturday's announcement was unlikely to lead to any tangible progress in relations between the Houthis and the government.
"There have been no negotiations to follow up this initiative," Vall said.
"People in the capital [Sanaa] are speculating there may be some secret talks going on, but there is no evidence this offer has been discussed or co-ordinated at all."
The Yemeni government had also insisted that the Houthis end their attacks on or from the Saudi Arabian side of the border, a cessation which al-Houthi announced on January 25 after his fighters apparently withdrew.
"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," al-Houthi said.
However, the Saudi government claimed 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.
In order for Saudi Arabia to accept the Houthi ceasefire, Sultan said on Thursday that 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.