More than five million children risk famine in war-torn Yemen as food and fuel prices soar, Save the Children said Wednesday, warning an entire generation may face death and "starvation on an unprecedented scale".

The three-year conflict between Yemen's Saudi-backed government and Huthi rebels linked to Iran has pushed the already impoverished country to the brink of famine, leaving many unable to afford food and water.

"Millions of children don't know when or if their next meal will come," said Helle Thorning-Schmidt, CEO of Save the Children International.

"This war risks killing an entire generation of Yemen's children who face multiple threats, from bombs to hunger to preventable diseases like cholera."

The already dire humanitarian situation is being exacerbated by the battle for the lifeline port of Hodeida, which is threatening to disrupt what little aid is trickling into the country.

Located on Yemen's Red Sea coast, the city is controlled by the rebels and blockaded by Saudi Arabia and its allies.

Having already identified four million children at risk of starvation, Save The Children warned Wednesday another million could now face famine as the Hodeida battle escalates.

"In one hospital I visited in north Yemen, the babies were too weak to cry, their bodies exhausted by hunger," said Thorning-Schmidt.