As malnutrition spreads in sparsely populated areas of al-Tohaita, international aid has grown scarce, residents say.
Warring factions in Yemen have exchanged accusations of violating a 72-hour ceasefire that began just before midnight on Wednesday.
The Arab alliance has accused Houthi forces of breaching the truce by attacking several cities in both countries on Friday, while the rebel movement said their strikes were in response to a coalition attack in the border district of Shad.
No casualties were reported by either side.
The Arab alliance said in a statement on Saudi state news agency SPA that Houthi forces used rockets, shells and snipers to attack border cities inside Saudi Arabia in the Jizan and Nijran provinces.
The Saudi-led coalition also accused the Houthis of launching attacks on the Yemeni capital, Sanaa, and other provinces such as Taiz, Hajja, Shabwa, Mareb and Aden.
The alliance said it had responded to the Houthi attacks “according to the engagement rules and continuing to exercise the highest self-restraints towards the violations of the ceasefire”.
The United Nations announced the ceasefire between the parties earlier in the week. It has the possibility for extension if it holds.
The UN’s special envoy for Yemen urged both parties to show “restraint, avoid further escalation, and strictly adhere” to the truce on Friday.
Ismail Ould Cheikh Ahmed said in a statement that the ceasefire was “fragile but largely holding”.
The UN official is liaising with the parties in an attempt to extend the ceasefire in order “to create a conducive environment for a long-lasting peace” in Yemen.
Previous attempts to enforce a ceasefire in the country have so far failed, with the war intensifying after a round of peace talks in Kuwait ended in August without achieving a breakthrough.
The Arab coalition stepped up its air raids following the breakdown of talks, and cross-border attacks from Yemen also intensified.
Monday’s ceasefire announcement came just over a week after the coalition bombed a funeral hall in Sanaa, killing about 140 people, including prominent Houthi political figures.
The air strike, which the coalition blamed on mistaken information from loyalists of Saudi-backed Yemeni President Abd-Rabbu Mansour Hadi, drew international condemnation and led to pressure for a ceasefire from the US and Britain, key backers of the coalition air campaign.
The three-day truce was also called into effect to allow sorely needed aid deliveries, as millions remain homeless and without food.
The Arab coalition has thus far carried out hundreds of air strikes and provided ground troops to support Hadi’s forces. But it has failed to dislodge the Houthis and their allies from key areas including Sanaa.
The Houthis and their allies hold most of Yemen’s northern half, while forces loyal to Hadi share control of the rest of the country with local tribes.
Government forces have recaptured the south and east but failed to make any significant advances.
The war has killed at least 10,000 people, wounded more than 35,000 and displaced at least three million since March last year, according to the UN.