Yemeni government forces moved to within 10 kilometres of Sanaa on Monday after overcoming more than a year of fierce resistance to the east of the rebel-held capital.
The advance came after troops earlier captured several hills in the mountainous Nehem area, army Col Ado Mogali said in a statement on the military-run 26 September website.
The Iran-backed Houthi rebels had used their control of elevated positions, particularly Al Tabah Al Hamra, one of the highest hills in the area, to repel government forces.
Col Mogali said the gains had left the rebels without the "fortified pockets" provided by the rugged terrain.
"The armed forces passed the obstacles presented by the rugged hills and the narrow routes which were blocking the army vehicles. Now our forces will lead an offensive on open land with no hills and no mountains as before." he said.
The open terrain will allow government forces to move faster and to surround Houthi positions in scattered villages because they can approach them from different directions.
The 26 September websites said 25 Houthis were killed and dozens taken prisoner during the fighting on Monday.
Mahmood Al Humaidi, a journalist covering the battle, said troops that fought through the heart of Nehem had linked up with forces advancing along the highway linking the area to Marib province. They then pushed to Maswarah village, which lies eight kilometres from Nakeel Bin Gaylan, a mountain overlooking Sanaa.
Troops and fighters loyal to the government of president Abdrabu Mansur Hadi launched an offensive in Nehem in August 2016 after the failure of UN-sponsored peace talks in Kuwait.
The area is a key route to the capital, which was overrun by the Houthis since September 2014. A Saudi-led military coalition intervened in the conflict in March 2015 after the rebels forced Mr Hadi's government to flee Sanaa and began to expand their control across the country.
Backed by the coalition, government forces have taken control of much of southern Yemen since then. The army and allied fighters have made a series of rapid gains this month following the collapse of the Houthis' alliance with forces controlled by former president Ali Abdullah Saleh. The rebels killed Saleh on December 4, days after he called for talks with the Saudi-led coalition to resolve the conflict.
Yemeni troops on Friday drove the rebels out of the last area held by them in the southern province of Shabwa. That victory give them control of a vital route north into Marib, which is partly held by the rebels.
Government forces have also been advancing on the rebel-held port of Hodeidah on the Red Sea coast, capturing three districts in the south of Hodeidah province.
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