Reports coming out of Ma’rib suggest that the Yemeni troops made major advances in the district of Harib and managed to wrest control of a key crossing.
Scores of the militants were killed and injured during the attacks and large groups of them fled the battledfield, the reports added.
The Yemeni army has sent thousands of fighters to the province over the past couple of weeks to expel forces loyal to the ex-government.
Since March 2015, Saudi Arabia has been conducting a bloody military aggression in Yemen with help from its regional allies, and using arms supplied by its Western backers. The aim of the war has been to bring Yemen's former president Abd Rabbuh Mansour Hadi back to power and defeat the Houthi Ansarullah movement.
Yemeni armed forces have been boosting their military capabilities and responding to the attacks using domestic missiles and drones, and targeting sensitive oil installations and military sites deep inside the Saudi territory.
Since 2015, over 100,000 people have been killed, according to the US-based Armed Conflict Location and Event Data Project (ACLED).