Al-Iryani said the war will end if the group accepts to sign the truce.
"All this is happening while officials are trying to implement a new ceasefire deal," Al Jazeera's Hashem Ahelbarra, reporting from Sanaa, Yemen's capital, said.
"In a statement issued by the Houthis, they also accuse Saudis of attacks in many areas, firing more than 270 rockets and rounds of heavy artillery."
The Houthis say their community of Shia Muslims from the Zaydi sect suffer discrimination and neglect and that the Yemeni government has allowed Sunni conservatives influenced by the Saudi religious establishment too strong a voice in the country.
Yemen has come under international pressure of late to end the conflict quickly and free up resources to confront a separate threat from an al-Qaeda offshoot that has set up operations there over the past year.
Last week, the Houthis accepted a conditional ceasefire first issued by the Saleh government in September.
The plan called on the Houthi fighters to disarm, free hostages and clear mountain hideouts.
However, the government dismissed the offer and said it would halt military operations against the fighters only "under a certain framework."
It also added a fresh demand that the fighters vow not to attack Saudi Arabia.
'Signature on deal'
Al-Iryani, the presidential adviser, said if Abdul-Malik al-Houthi, the Houthis' leader, "signs this document and accepts its mechanisms, the war will stop immediately".
Our correspondent said: "All that is required of Abdul-Malik al-Houthi is to put his signature on the deal, but now the problem lies within the details of the ceasefire."
The peace proposal calls for the formation of five committees made up of Houthi and government representatives that would implement the ceasefire, al-Iryani said.
The committee on border security would also include Saudi officials.
Neighbouring Saudi Arabia was drawn into the conflict in November after the Houthis crossed the border and killed two Saudi border guards.
At least 133 Saudi soldiers have died in the fighting.
The fighters announced a unilateral ceasefire with Saudi Arabia in late January.
However, the Saudis responded cautiously to the group's announcement and demanded fighters pull back from border positions and return five missing soldiers.
Several earlier ceasefires quickly disintegrated, mainly because the Houthis said their demands were not addressed.
In what could deal a further blow to the peace process, a security court in Sanaa on Saturday sentenced Yahya al-Houthi, the brother of Abdul-Malik al-Houthi, in abstentia to 15 years in prison on charges of supporting the uprising.
Yahya al-Houthi has been living in Germany for the past three years.