The rebels, known as Huthis, have been facing fierce resistance from Al-Qaeda fighters and Sunni tribesmen as they seek to expand their territory after seizing the capital Sanaa and the Red Sea port city of Hudeida.
Heaving fighting erupted in the central town of Rada, a mixed Sunni-Shiite area that has been the scene of frequent clashes.
The rebels were killed in a car bombing that targeted a building where they had gathered and in subsequent clashes, tribal and security sources told AFP, adding that 12 rebels were also captured by Al-Qaeda militants.
The Al-Qaeda militants also attacked rebel positions northeast of Rada and along a road connecting the town in Baida province to neighbouring Dhamar, a Shiite-populated province taken last week by the rebels.
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The Huthis have seized on chronic instability in Yemen since the 2012 ouster of veteran strongman Ali Abdullah Saleh to take control of large parts of the country.
President Abdrabuh Mansur Hadi's weak Sunni-led central government has failed to stop the rebels, despite a UN-brokered peace deal that was supposed to see them withdraw from the capital.
The fighting has raised fears of Yemen -- located next to oil kingpin Saudi Arabia and important shipping routes in the Gulf of Aden -- collapsing into a failed state.
Hadi's government is also a key US ally in the fight against Al-Qaeda, allowing Washington to conduct a longstanding drone war against the group on Yemeni territory.
The rebels faced no resistance when they took control of Sanaa last month and have refused to leave despite appearing to agree to the naming of a new prime minister under the UN deal.