The waterway connects the Suez Canal and Red Sea with the Gulf of Aden and the Indian Ocean beyond and is a major shipping lane.
"We launched an offensive which enabled us to recapture two mountains," loyalist commander General Fadhl Hassan told AFP.
"In 18 hours of fighting, which reduced in intensity this afternoon, 13 rebels and four of our men, one of them a colonel, were killed."
The rebels said on their sabanews.Net website that they had taken several government-held positions and inflicted losses in the fighting.
The fighting came as the rebels marked the second anniversary of their seizure of the capital Sanaa in alliance with renegade troops loyal to ousted president Ali Abdullah Saleh.
Celebrations were also planned in the rebel-held Red Sea port of Hodeida.