Yemen's government says its troops have killed 20 members of the northern Houthi insurgency. The latest clashes come as both the government and rebels offer conditions for ending the nearly six-year conflict.
Yemen media report fighting in the northern provinces of Malahidh and Saada.
Government officials say they are rejecting the latest Houthi offer to accept the government's ceasefire plan because the rebels failed to agree to all the terms.
A statement Saturday attributed to rebel leader Abdul-Malik al-Houthi said his fighters would accept five of the government's demands.
The message, posted on the internet, said the rebels wanted the bloodshed to end, and called on the government to place national interests first.
Government officials said the Houthis failed to say they would stop their attacks against Saudi forces across the Yemen border. Last week, the rebels announced a cross-border truce, but Saudi officials said rebel snipers remained on their territory.
Shi'ite Houthi rebels have complained that Yemen's central government discriminates against them. A variant of that refrain is echoed in the south, where a secessionist movement is strong.
Foreign powers have been paying increasing attention to the poorest Arab nation, where they argue the chaos is making it easier for al-Qaida militants to set up base.