"The airstrikes targeted the reinforcements on Saturday evening at the frontline of Rahabah district, destroying four pick-up vehicles and killing more than 20 people," the source told Xinhua news agency on Sunday.
Meanwhile, the Houthi-run al-Masirah TV on Saturday reported 17 airstrikes on frontlines of Marib's western districts of Rahabah, Jabal Murad and Sirwah, without providing further details.
Last week, the Houthis advanced into al-Kulah, the centre town of Rahabah district, after deadly fighting with the government troops.
The Iran-backed Houthi militia launched in February a major offensive on Marib in an attempt to seize control of the oil-rich province, the last northern stronghold of the Saudi-backed Yemeni government.
The UN has warned that the offensive on Marib, which hosts nearly 1 million internally displaced people, could lead to a major humanitarian catastrophe.
The world body's recent peace proposal to end the war was publicly rejected by the Houthi group.
Yemen's civil war flared up in late 2014 when the Iran-backed Houthi group seized control of much of the country's north and forced the internationally recognised government of President Abd-Rabbu Mansour Hadi out of the capital Sanaa.
The Saudi-led coalition intervened in the Yemeni conflict in March 2015 to support Hadi's government.