After days of deadly fighting, the Yemeni army has recaptured a chain of strategic mountains near the southeastern tips of the Houthi-held capital Sanaa, a government military source said Sunday.

"The army forces backed by Saudi-led coalition warplanes pushed back the Iran-backed Houthi rebels from the chain of Al-Abzakh mountains in Rahabah district southwest of Marib Province," the source in Marib said.

According to pro-government local media, the army during the week-long fighting also recaptured many areas north and east of Al-Abzakh mountains in Rahabah district.

"The rebels fled, leaving behind heavy weapons. Now most of Rahabah district is under the army control," the source said on condition of anonymity.

Meanwhile, the Houthi-run al-Masirah TV reported 29 Saudi-led airstrikes on Rahabah district over the past two days, without providing further details.

The Houthis began in February a major offensive on Marib in a desperate attempt to seize control of the oil-rich province, the government's last northern stronghold.

The United Nations has warned that the offensive on Marib, which hosts nearly 1 million internally displaced people, could lead to a major humanitarian catastrophe.

Yemen's civil war flared up in late 2014 when the Houthi group seized control of much of the country's north and forced the internationally recognized government of President Abd-Rabbu Mansour Hadi out of Sanaa.

The Saudi-led Arab coalition intervened in the Yemeni conflict in March 2015 to support Hadi's government.