The rebels, known as Huthis or Ansarullah, had travelled to Amran to take part in a demonstration, but a gun battle broke out when they insisted on crossing a checkpoint to the northern entrance to the city with their weapons, the official said.
Seven more rebels were wounded in the ongoing clashes, the Huthis said, and the security official said two soldiers were also hurt.
Last week, Huthis armed with assault rifles, marched in Amran along with vehicles mounted with rocket launchers, demanding the sacking of the "corrupt government".
Last month, President Abdrabuh Mansur Hadi and party leaders in Sanaa agreed to transform the country into a six-region federation as part of a political transition.
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The rebels, who complain that Yemen would be divided into rich and poor regions under the plan, have been trying to enlarge their zone of influence by pushing out from their mountain strongholds in the far north to areas closer to the capital.
In early February, they seized areas in Amran province, leaving more than 150 people dead in fighting with local tribes.