Fighting erupted a day after UN envoy Martin Griffiths told the security council warring sides made "significant progress" in agreeing on a ceasefire amid a burgeoning Covid-19 outbreak.
The Yemeni army announced on Friday that scores of Houthi militia members were killed in clashes in al Bayda governorate.
The press office of the Yemeni military said many Houthis were also injured in the fighting.
The Houthis have yet to comment on the incidents which occurred a day after UN Yemen envoy Martin Griffiths told the Security Council that the warring sides made "significant progress" toward agreeing on a ceasefire.
Griffiths made a renewed push for a truce in Yemen after a call by UN Secretary-General Antonio Guterres on March 23 for a ceasefire in global conflicts so the world can focus on fighting the coronavirus pandemic.
He gave the government of Yemen and the Houthi group –– who have been fighting for more than five years –– draft proposals on a nationwide ceasefire, humanitarian and economic measures, and the urgent resumption of the political process.
"We have seen significant progress on these negotiations, in particular with respect to the national, nationwide ceasefire," Griffiths told the 15-member Security Council.
"However, the ceasefire is part of the broader package that needs to be agreed in full. And differences remain on some of the humanitarian and economic measures in that package," he said.
Griffiths said those humanitarian and economic measures were also needed to combat the coronavirus "which is spreading at an unknown rate, given very low levels of testing".
Fear of hunger
Around 24 million people in Yemen need humanitarian aid and aid groups fear a catastrophic outbreak of the coronavirus given Yemen's shattered health system and the widespread hunger and disease after years of conflict.
Deputy UN aid chief Ramesh Rajasingham said there were so far 72 confirmed cases of the coronavirus, including 13 deaths.
The coronavirus pandemic has killed more than 302,000 people globally.
Yemen has been mired in conflict since the Iran-allied Houthi group ousted President Abd Rabbu Mansour Hadi's government from the capital Sanaa in 2014.
A Saudi-led military coalition in 2015 intervened in a bid to restore the government.
"The people of Yemen are right to be frustrated about the slow pace of these negotiations. We all hope to see these negotiations soon come to a successful close," Griffiths said.