A purported rebel spokesman had, however, described a defence ministry statement on December 20, which said that Abdul-Malik al-Houthi had been badly wounded, as "baseless".
Abdulghani al-Iryani, a political analyst based in Sanaa, said that if the reports of al-Houthis death were true they could extend the conflict.
"It is a complication that comes at the worst possible time," he told Al Jazeera.
"The war in Saada [where Yemeni forces are battling Houthi fighters] could have been stopped by this time because Abdul-Malik al-Houthi had agreed to the five conditions set by the government for a ceasefire.
"All he needed to do was make a public statement to that effect. If he is now dead, then there will be a power vacuum in the leadership of al-Houthis that will postpone that possibility."
The fighters, who launched a rebellion against the Yemeni government in 2004, belong to the minority Zaidi sect of Shia Islam and complain of social, economic and religious marginalisation.
Government forces launched "Operation Scorched Earth" on August 11 in an attempt to crush the rebels in the mountainous northern region.
The Yemeni government says the rebels are receiving support from Iran, although Tehran has denied any involvement in the fighting.
Sanaa has also recently claimed that the Houthi are working with predominantly Sunni Muslim al-Qaeda fighters in Yemen, but the group has dismissed the allegations.
"The allegation about our relationship with what is called the al-Qaeda group is a fabricated lie and defamation," the group said in comments emailed to the Reuters news agency earlier this week.
Meanwhile, al-Qaeda in the Arabian Peninsula said in comments posted on a website that it will take revenge against the US over air raids in Yemen that it claims killed about 50 people.
"We will not let Muslim women and children's blood be spilled without taking revenge," a statement dated December 20 said.
The group has said that the raids were carried out by five US warplanes, but the Yemeni government has said that it launched the attacks with aircraft and ground forces to foil planned suicide bombings.