The fighters - followers of the Zaidi offshoot of Shia Islam that is unique to Yemen - hope to reinstall the Shia imamate that ruled the country for hundreds of years before being overthrown in 1962.
Saada, the focus of the revolt and the scene of much of the recent fighting, has traditionally been the centre of Zaydism which is followed by around 20 per cent of Yemen's population.
On Friday, the Yemen Times had reported that the government had carried out intense air raids and mortar bombardments of fighter-held areas surrounding the city.
Also on Friday, Yemen said it was recalling its ambassadors to Iran and Libya, amid accusations that the two countries were aiding the Zaidi Shia forces.
Meanwhile Yahya al-Houthi, the exiled brother of the founder of the rebel movement, said that the group was willing to lay down its arms in return for an amnesty, as proposed by Abubakr al-Qirbi, Yemen's foreign minister, a few days previously.
"This call is in the right direction, and there is no reason to launch this huge war against us," al-Houthi said in a statement issued in Germany and faxed to reporters in Yemen.
"We and our supporters are ready to obey the state provided that the state ... carries out its responsibilities towards the citizens."
The present conflict began in 2004 when Hussain Badr al-din al-Houthi, Yahya's brother, led an armed uprising against the government.
The fighting has continued on-and-off since then, punctuated by government amnesties which the rebels have used to rearm and which the army has used to advance deeper into rebel-held territory.