The government in Sanaa responded on the defence ministry website, saying that the conditions for the truce had not been met.
"They haven't opened the roads, evacuated their positions or freed captured civilians and soldiers," the statement said on the 26sep.net ministry website.
The Eid ceasefire is the second to fail in as many weeks, and comes as government forces appear to be making little progress in the conflict.
Earlier, responding to the truce offer, Muhammad Abdulsalam, a spokesman for the Houthis, had said that they were willing to comply with the government's five conditions if the authorities were seriously committed to the truce.
Speaking to Al Jazeera, he said "we are ready to examine them, and that is natural".
With no end in sight to the fighting, UN aid agencies say thousands are staying in tented camps in mountainous territory.
|Footage released by the Houthis suggests a recent government air raid killed civilians
They launched an appeal in Geneva last month for $23.5 million to help the displaced Yemenis.
In the most recent fighting, the army carried out three air raids and blew up houses in Saada city - under government control - on Friday.
About 87 people died on Wednesday in an air raid at a makeshift camp for displaced persons in Harf Sufyan in Saada.
The Houthis released a video on Saturday purporting to show some of the victims of the Harf Sufyan raid, women and children among them.
The unverified video appears to show the victims being laid to rest in communal graves.
Navi Pillay, the chief of the UN human rights commission, said in Geneva that an inquiry into the air raid should take place and called the casualty reports "deeply disturbing".
The rights body called on Yemen to investigate the air attack.
A separate statement released by Ban Ki-moon's office said "the [UN] secretary-general is deeply concerned about reports of recent air strikes during the course of military operations in the north of Yemen and the reported civilian casualties resulting from this".
The Houthi fighters, who are led by Abdul-Malek al-Houthi, are concentrated mainly in the Saada and Amran provinces.
They are known as Houthis after their late leader, Abdul-Malek's brother Hussein Badr Eddin al-Houthi, a Zaidi leader who was killed by the Yemeni army in September 2004.
An offshoot of Shia Islam, the Zaidis are a minority in mainly Sunni Yemen but form the majority in the north.
The government accuses the Houthi fighters of seeking to restore the Zaidi Shia imamate which was overthrown in a 1962 coup that sparked eight years of civil war.
But only a small minority of Zaidis are in involved in the Houthi uprising.