Battles raged over the weekend around the government-held city of Marib, killing 76 Houthi fighters, a pro-government spokesman told The National on Sunday.
Since February, the Iran-backed Houthis have been trying to seize Marib, the capital of the oil-rich region and the government’s last significant pocket of territory in the north.
At least one child was killed and five wounded in rebel shelling.
The Saudi-led military coalition entered the Yemen conflict to support the internationally recognised government in 2015.
On Sunday it launched air strikes that killed 23 Houthis, raising the overall death toll among the militia fighters to 76 on Saturday, the spokesman said.
The rebels “are launching simultaneous attacks” in the areas of Kassara and Al Mashjah, north-west of the city, and in Jabal Murad in the south, a military official told AFP.
“They have made progress on the Kassara and Al Mashjah fronts, but they have been thwarted on the Jabal Murad front,” he said.
Saudi Arabia has also been thwarting near-daily attacks by Houthi drones and missiles, with the latest drone launched at the southern Saudi city of Khamis Mushait, state media reported.
In late 2014, the Houthis overran the Yemeni capital Sanaa, 120 kilometres to the west of Marib, along with much of northern Yemen.
The loss of Marib could lead to a humanitarian disaster, as more than two million civilians displaced from fighting elsewhere have sought refuge in and around the city.
About 140 sites have sprung up in the region to provide basic shelter for up the displaced, Yemen’s government said.
The rebels have increased missile and drone strikes against neighbouring Saudi Arabia in recent months, demanding the opening of Yemen’s air space and ports. They have rejected Riyadh’s proposal for a ceasefire.
Last month the UN condemned the escalation and said a humanitarian disaster loomed.
The UN Security Council said the fighting “places one million internally displaced persons at grave risk and threatens efforts to secure a political settlement when the international community is increasingly united to end the conflict”.
US Secretary of State Antony Blinken said the suffering would end only when a political solution between the Houthis and the internationally recognised government was found.
The conflict in Yemen has killed tens of thousands of people and pushed millions to the brink of famine, in what the UN has described as the world’s worst humanitarian crisis.