Government mounts Iron Fist campaign against armed Zaydi Shia group in Saada province.
But the government, which is supported by Saudi Arabia, accuses them of being loyal to Iran.
Under truce conditions announced by the country’s supreme security committee headed by Ali Abdullah Saleh, the fighters were told they must evacuate all occupied government offices, hand in ammunition and equipment and free prisoners.
The committee said authorities would stop the military offensive and release all detainees seized on suspicion of having links to the Houthis if they complied, the official Saba news agency said on Thursday.
The committee also demanded information on the whereabouts of a British and five German expatriates who were seized in June.
The six were seized along with three women, two Germans and a South Korean, who were later found dead.
The fighters have denied government claims they are holding the group.
Al-Houthi rejected the conditions in a statement, saying the government was seeking to “mislead the public opinion” by setting them.
“Authorities are not actually seeking a radical settlement for this issue … and their conditions are merely intended to mislead the public opinion after the crimes against humanity they committed in Saada villages.”
He called on the government to comply with a ceasefire agreement signed by the two parties in Doha, the Qatari capital, in June 2007.
At least 19 fighters and civilians were killed on Wednesday after the army bombarded strongholds of the Houthis on the border with Saudi Arabia, both fighers and residents said.
Scores of people were injured.
The offensive included aerial, artillery and missile strikes on the strategic heights of Matra and Dhahian, the two main strongholds of the Houthi fighters, on the border with Saudi Arabia.
Tensions have been rising between the Houthis and the army in Saada since last July when President Saleh declared the conflict over.
Five waves of conflict between the Houthis and the military have left hundreds of soldiers and fighters dead since 2004.
Authorities have accused the Houthis of trying to reinstall the rule of imams, toppled by a republican revolution in northern Yemen in 1962.