Clashes flared this week around the Red Sea port of Midi and the nearby Saudi border town of Huthaira, spilling over into the rebel heartland of Saada inland.
The Yemeni army officers said loyalist forces had managed to wrest control of several rebel-held towns straddling the border.
Saudi officials contacted by AFP did not respond to requests for comment.
The rebels control most of northern Yemen, including the Red Sea coast.
But the government controls several pockets near the Saudi border, including the port of Midi.
More than 8,500 civilians have since been killed, with both sides in the conflict being accused of not doing enough to avoid civilian casualties.
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