A Saudi-led coalition has been fighting the Houthi movement in Yemen since it intervened there in 2015 to restore the internationally recognised Yemeni government in exile.
A Yemeni military source confirmed the report to AFP.
Fresh clashes later erupted between UAE-backed government forces and the Iran-allied rebels on a road linking the airport to Hodeida port on the Red Sea coast, a Yemeni army source said.
During the press conference, Colonel al-Maliki reviewed the efforts of the Coalition Forces in terms of securing the work of the global and worldwide humanitarian organisations in all Yemeni territories, protecting the roads and corridors of the comprehensive humanitarian operations plan in Yemen and granting permits for relief and humanitarian aid through land, air and sea, which last week included 65 flights, carried more than 4,000 passengers, 41 permits for ships anchored in all Yemeni ports, and one for the shipment of aid arriving by road.
United Nations officials estimate that in a worst-case scenario the fighting could cost up to 250,000 lives, especially if a cholera epidemic occurs in the widely impoverished region.
In an interview with Lebanon's al-Mayadeen television network, she added that most of the fighting had been restricted in the Doreihami front, outside the port city, as for Tuesday.
On Tuesday, the UN's World Food Programme hurriedly unloaded three ships full of food aid - enough, it said, to feed six million people for one month. Aramco said its facilities are safe and operating normally after the Houthis' statement, Reuters reported. "The streets are nearly empty, deserted", he said, adding that most were heading for Sanaa, Raymah and Wusab, in Houthi-controlled areas inland.
"The political moves that are being proposed are being supported by us. but the situation is now very volatile", he said. The offensive has been backed by the United Arab Emirates (UAE). Hodeida is the main entry point for food to Yemen, already on the brink of starvation.
The United Nations has warned that an attack on the port itself could cripple shipments of desperately needed aid to the 8.4 million Yemenis facing imminent starvation.
Most of these missiles were intercepted by Saudi air forces, but a few fell into residential areas and caused casualties and damage. It could also give an edge to the Western-backed military alliance which, despite superior weaponry and firepower, has failed to defeat the group in a war that has killed 10,000 people.
A member of the Houthis' ruling politburo, Mohammed al-Bukhaiti, denied the talks with Griffiths had focused on handing over Hodeidah "because this request is unrealistic".