In a direct call to al-Huthi on Sunday, President Ali Abd Allah Salih told local media that he wants an end to the 'bloodshed'.
"I call on you to surrender and I guarantee a fair process in the accusations against you," he said.
Salih was speaking a day earlier during a meeting with religious officials, who he said could appoint "a lawyer to defend al-Huthi."
Clashes erupted on 18 June in Sada province near the border with Saudi Arabia.
The heavy fighting is said to have killed some 118 people, including 86 of al-Huthi's supporters and 32 soldiers including policemen, interior minister Rashad al-Alimi said on Saturday.
Fighting continued to rage on Saturday, with both sides reporting more deaths.
Aljazeera’s correspondent in Sanaa reported heavy fighting between Yemeni security forces and al-Huthi supporters.
Official estimates put the number of deaths at about 118 and another 141 wounded.
According to an unconfirmed report by a military official who spoke on condition of anonymity, Hussain al-Huthi's brother Badruddin al Huthi, had been killed by a raid on the 'mountainous hideout'.
"We bombarded the nountain with heavy artillery and Katyusha rockets. Their resistance is diminishing and they will surrender when they run out of supplies"
Yemeni military official
"We bombarded the mountain with heavy artillery and Katyusha rockets. Their resistance is diminishing and they will surrender when they run out of supplies", the official said.
Various sources told Aljazeera that "many of al-Huthi's supporters had withdrawn and are repositioning".
On the other hand government sources say the long-term preparations al-Huthi has already taken and the mountainous terrain, places them (al-Huthi supporters) in an ideal position to engage government forces for a much longer period than expected.
According to official reports, "al-Huthi does not have much public support" while local sources say he had an influence in Sada particularly during the last three years.
"During that time he could have attracted many youths by the religious lectures and lessons he was giving in schools that he had established", government sources told Aljazeera.
Huthi is a preacher from the Zaidi community, a minority Shia Muslim group, dominant in northwestern Yemen.
Yemeni authorities accuse him of 'organising protests against the US and Israel.
Since the 11 September 2001 attacks in the US, Yemen has launched a major crackdown against alleged Al-Qaida sympathisers.