"Dozens of people have been killed and wounded in both camps," the spokesman said without elaborating. No official confirmation of the toll was available.
Sanaa had announced a unilateral ceasefire in its Scorched Earth offensive against the Houthi fighters on Friday. The move was intended to allow humanitarian aid into a conflict zone that has created thousands of refugees.
However, poor communication between the rival factions meant that the truce had little chance of holding.
Al Jazeera's correspondent said various units in the remote and mountainous terrain may not have even known a ceasefire had been declared.
Thousands displaced
The war has triggered a humanitarian crisis which is attracting the world's attention only now.
The International Committee of the Red Cross (ICRC) said on Thursday that more than 25,000 people had registered as displaced in Saada and Amran.
"The dire humanitarian situation is hitting women and children especially hard," Daniel Gagnon, an ICRC official working in Yemen, said.
Other people are said to have fled as far as Sanaa, the capital in the country's south, more than 185km away.
Abdel Malik al-Houthi, the Houthis' leader, on Saturday said that displaced people should return to their homes and villages. He also called on the government to give guarantees to civilians in the north that their homes would not be targeted.
Aid agencies from the UN estimate that more than 100,000 people have been forced to flee their homes.
Fighting reignited in the north last month and has continued primarily in Saada, on the Saudi Arabian border.
Zaidi Shia Muslims are fighting for independence from a government which they say is corrupt and too close to Saudi Arabia.
Both sides have already rejected ceasefire offers from the other party.
An offshoot of Shia Islam, Zaidis are a minority in mainly Sunni Yemen but form the majority community in the north, some of whom want a return to the imamate, which was overthrown in a 1962 coup.
The conflict first began in 2004.