Government forces advanced a few kilometres following fierce battles south of the city, one of the officials said.
A senior military commander was killed in clashes between Yemeni government forces and Houthi rebels attacking the central city of Marib.
Major General Nasser al-Zubiani, who headed military operations of the government’s armed forces, was killed on the front line in the Balaq mountain range, south of the city of Marib, said two officials, speaking on condition of anonymity because they were not authorised to talk to the media.
Al-Zubiani was inspecting government troops and allied tribal fighters trying to stave off the Houthi attack at the time.
Government forces had earlier advanced a few kilometres following fierce battles south of the city, one of the officials said.
The rebels stepped up attacks on Marib in recent weeks, sending waves of fighters to try and breach government defences. Hundreds died in the clashes, mostly rebels, the official added.
A Saudi-led coalition, which is fighting on the side of the government forces, said it launched at least 35 air strikes on rebel positions around Marib over the weekend, killing at least 200 Houthis.
At least three more air strikes hit the rebels in Yemen's western coast, it said.
The Houthi offensive on Marib came as they suffered blows elsewhere in the country.
Last month, government forces took the district of Hays and a major highway linking the contested port city of Hudaida with the rebel-held capital of Sanaa.
Yemen’s civil war began in 2014 when the Houthis took Sanaa and much of the northern part of the country, forcing President Abd Rabbu Mansour Hadi’s government to flee to the south, then to Saudi Arabia.
The Saudi-led coalition, backed at the time by the US, entered the war months later to try restoring Hadi to power.
Despite a relentless air campaign and ground fighting, the war has deteriorated into a stalemate, killing more than 130,000 people, both civilians and fighters, and spawning the world’s worst humanitarian crisis.