It has not been possible to be independently verify those reports.
Yemen, one of the poorest Arab countries, faces several challenges to its political stability, including rising secessionist sentiment in the south and periodic attacks by al-Qaeda.
The military offensive in the north was ignited after the Zaydi sect, a part of Shia Islam, to which the fighters belong, claimed to be gaining greater control of the northern Saada province, which borders Saudi Arabia, from government troops.
The fighters, led by by members of the al-Houthi family, including Abdul-Malik al-Houthi, have recently accused government forces of using white phosphorous in their bombardments of the north.
The government has denied those reports and says it does not even have phosphorous weapons in its arsenal.
White phosphorous is banned under international law for use against non-combatants because it causes severe burns.
Mohammad al-Qadhi, a foreign correspondent based in the Yemeni capital Sanaa, told Al Jazeera: "These allegations have been reported by some media outlets, but they have been strongly denied by the ministry of defence."
Mohammad Nasser Ahmed Ali, Yemen's defence minister, said on Sunday that the army had hit hard at the Houthi fighters.
"The elements of rebellion and terrorism in Saada ... have been hit hard today by the army," he said in an address to a military academy.
"They have incurred heavy losses and have been paralysed."
Government forces "have captured some of the rebels who will be brought to justice," he said without specifying the number of captive Zaidi fighters, also known as Houthis.
A Houthi leader and eight others were killed in fierce clashes during the day in the Harf Sufyan area of Amran province, south of Saada, local sources said.
Government forces have been trying since Thursday to open the road linking Saada to the capital Sanaa after rebels blocked it at Harf Sufyan, the defence ministry website quoted Sheikh Kahlan Abu Shawarib, mayor of Amran, as saying.
At least two soldiers and 16 rebels were reported killed on Friday.
Fighting between the Houthis and the military has left hundreds of soldiers and fighters dead since 2004.