Fighting is said to have erupted near the town of Harad which was captured by government forces two days ago.
Military sources said 28 troops were killed while Houthi rebels said they had lost 40 fighters.
Clashes have continued despite a UN-backed ceasefire and peace talks in Switzerland which began on Tuesday.
As well as those killed on Saturday, at least another 50 rebels and 40 pro-government troops were reported to have been wounded.
Tribal sources said there was an upsurge in fighting early on Saturday as government forces - which are being backed by a Saudi-led coalition - advanced towards the Red Sea port of Midi and rebels brought in reinforcements.
Houthi and government delegates have been meeting in Biel in Switzerland to try to end months of fighting.
Rebels have accused Yemeni and Saudi-led coalition forces of repeatedly breaching the ceasefire, which is meant to last for a week.
The Saudi-led coalition launched a military campaign in March in support of the government after Houthis seized the capital, Sanaa, and advanced towards the second city of Aden.
Since then, at least 5,700 people, almost half of them civilians, have been killed in air strikes and clashes on the ground.
The humanitarian crisis in Yemen has also worsened, with more than 21 million people - four-fifths of the population - now in need of aid.

The soldier, who has not been named, died after the device detonated in Ayn Issa, north of the IS stronghold Raqqa.
It is the first such death since US special forces deployed in Syria in October 2015.
Meanwhile at least 32 people have been killed in intense Syrian air strikes on rebel-held east Aleppo, monitors say.
The UK-based Syrian Observatory for Human Rights, which monitors casualties, said the attack was one of the heaviest since Syrian forces resumed an offensive on the east earlier this month.
A statement from the anti-IS US-led coalition said the serviceman died on Thursday from wounds sustained in the blast.
Coalition commander Lt Gen Stephen Townsend called the soldier a "hero" and praised those he said were protecting his country from IS's "hateful and brutal ideology".
"On this Thanksgiving, please be thankful that there are service members willing to take up the fight to protect our homeland," he said.
US Defence Secretary Ash Carter said the soldier's death was a "painful reminder of the dangers our men and women in uniform face around the world to keep us safe".
About 300 US special forces personnel have been deployed in Syria to advise an anti-IS alliance of Arab, Kurdish and other fighters, and improve the coalition's targeting of air strikes.
Meanwhile, the Syrian government has intensified its offensive on east Aleppo, monitors and activists say.
"There was an escalation in the evening, with successive bombardments," SOHR director Rami Abdel Rahman told AFP news agency, adding that many people were trapped under rubble.
Five children were reported to be among the dead.
Syrian forces stepped up ground and air attacks on eastern Aleppo in November following a three-week moratorium.
Once Syria's commercial and industrial hub, Aleppo has been divided roughly in two since 2012, with the government controlling the west and rebels the east.
In late September, two weeks after encircling the east and reimposing a siege on its estimated 275,000 residents, the army launched an all-out assault to take full control of the city.
Rebels launched a counter-attack in an attempt to break the siege in late October. But their progress slowed after early gains.
At least 68 people are reported to have been killed in fresh clashes between government troops and Houthi rebels in north-west Yemen near the Saudi border.
[NEXT_CONCEPT]
A US serviceman has been killed by an improvised explosive device while fighting against so-called Islamic State (IS) in Syria, officials say.