Houthi fighters attacked government troops in al-Malahid, in Saada, and in Harf Sufian, a district in neighbouring Amran province, a spokesman for Yemen's senior security commission said in a statement published early on Saturday.
The reported violations occurred nearly three hours after the truce took effect at 1800 GMT on Friday to allow humanitarian operations for about 150,000 people forced from their homes by intense fighting.
"Despite declaring their obligation to the ceasefire, the terrorist elements continued their acts of sabotage in the al-Malahid sector and some areas of Harf Sufian," the statement, which was carried by the official Saba news agency, said.
It said the fighters "bear the responsibility for all consequences of those violations".
Authorities said the ceasefire was ordered in response to appeals from international and local aid agencies as well as residents of Saada and after the group had agreed to stop attacks against government troops and to clear landmines from roads.
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.
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.