Yemen's Huthi rebels suffered 30 fatalities in the clashes, which took place 2 kilometres from Hodeida airport, south of the city, medical sources said.
Nine pro-government troops were killed in the same area, the medics said. Military sources said the deaths were caused by mines and snipers.
A correspondent behind the government lines in Al Duraihimi witnessed ambulances arriving from the front loaded with dead and wounded.
Saudi-led coalition launches attack on Yemen's Hodeidah
Saudi-led coalition warplanes and Apache helicopters provided "continuous" air support to pro-government forces, striking Huthi positions, military sources said.
The Huthis have put up a fierce resistance, however, using snipers to slow the assault, the sources added.
The coalition-backed troops have also been slowed by the need for de-mining operations to advance.
The government side sent significant reinforcements to the front on Thursday, according to military sources.
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