An international aid group is warning that escalation of fighting around Yemen's port city of Hodeida threatens to cut off essential supplies to millions of people in the war-ravaged country.

Muhsin Siddiquey, Oxfam's chief in Yemen, said on Wednesday that if the Hodeida port is blocked, "the result will be more hunger ... and more families burying their loved ones."

Oxfam says fighting between pro-government forces and Shiite rebels has already forced hundreds of families to flee their homes.

Government forces have been trying to seize rebel-held Hodeida, a vital lifeline from which most of Yemen's population gets food and medicine.

Yemen's civil war has raged since March 2015 between Houthi rebels and government forces backed by a Saudi-led coalition. The war has pushed Yemen to the brink of famine.