Senior U.S. diplomats are holding talks in the Gulf region in a renewed push for a ceasefire in Yemen as fierce ground battles spread and the Iran-aligned Houthi group resumed cross-border attacks on Saudi Arabia after a brief lull over Muslim holidays.

U.S. special envoy for Yemen Tim Lenderking arrived in Saudi Arabia on Tuesday following a visit by Deputy Secretary of State Wendy Sherman to Oman, amid stalled efforts for a breakthrough in ending more than six years of war.

The Saudi-led coalition that backs Yemen's recognised government and the Houthis have been at odds over a United Nations-led proposal for a nationwide truce and the lifting of a coalition blockade to ease a dire humanitarian crisis.

Meanwhile battles are raging in Yemen's gas-rich Marib region, the government's last northern stronghold, and in al-Bayda governorate. The coalition said late on Tuesday it destroyed four Houthi ballistic missiles and two drones launched towards Jizan in southern Saudi Arabia.

Fighting has spread to al-Bayda as Houthi forces try to advance towards the southern oil-producing Shabwa region, local and military sources said. Coalition air strikes have so far repelled Houthi advances.

Lenderking will discuss "growing consequences" of the Marib offensive that is triggering instability elsewhere and the "urgent need" for Riyadh and the Saudi-backed government to facilitate fuel imports to northern Yemen, the State Department said.

The Houthis have insisted sea and air restrictions on areas they control be removed before any ceasefire talks, while the coalition wants a simultaneous deal.

The Houthi movement holds most big urban centres after ousting the government from the capital, Sanaa, in late 2014, which prompted the coalition to intervene months later in a conflict widely seen as a proxy war between Saudi Arabia and Iran.

The war has killed tens of thousands of people and pushed Yemen to the brink of famine. The Houthis say they are fighting a corrupt system and foreign aggression.

Reuters