The group of anti-government fighters, led by Abdul-Malik al-Huthi, said earlier this week that tribal mediation had brought an end to the fighting between the two sides which signed a Qatari-brokered peace deal in June 2007.
But shortly after Saleh made his remarks, military sources in the province told the AFP news agency that fighters had launched an assault on the village of Mahza, east of the town of Saada, and had seized control of the area.
On Wednesday, the defence ministry said a local council official and his two bodyguards were killed in Al-Jawf province, southeast of Saada. Tribal sources said that armed tribesmen retaliated by attacking the rebels, killing a local commander.
The group has been fighting to restore the Zaidi imamate which was overthrown in a 1962 coup. Zaidis are a minority in mainly Sunni Yemen but the majority in the northwest regions.
The fighters want Zaidi schools set up in Saada and say they are defending their villages against government oppression.
Saleh is himself a Zaidi, but the group rejects his government as illegitimate and opposes his alliance with the United States.
Each side has accused the other of reneging on the peace deal accord requires the government to release rebel prisoners, dismantle roadblocks and withdraw troops from areas of Saada province in return for the group's disarmament.
Saleh made the comments during the launch of a programme of youth summer activities as he marked his 30th year as the country's leader.
He first took power in 1978 as the leader of the then North Yemen and steered the country to reunification in 1990 as the communist south's sponsor, the Soviet Union, headed for collapse.