Pro-government forces in Yemen, backed by a Saudi-led coalition, have launched air strikes on the airport that serves the key port city of Hudaydah.
They have also been fighting Houthi rebels on the ground with mortar fire.
The pro-government forces said they had taken control of the airport on Saturday, but the rebels denied this.
Meanwhile the UN envoy to Yemen is holding a second day of talks in the capital Sanaa, aimed at securing a rebel withdrawal from Hudaydah.
Martin Griffiths is believed to have put forward a plan guaranteeing the safety of Houthi fighters if they pull out, leaving the harbour to be operated by the UN.
The only major port controlled by the Houthis, Hudaydah is seen as a lifeline for millions of Yemenis at risk of famine.
The Houthis’ Saba news agency said the coalition had carried out five air strikes on the city. Saudi-owned al-Arabiya TV also said the airport had been hit.
The Houthis are demanding an end to the air strikes.
The Hudaydah offensive, which is being directed by the United Arab Emirates, began on Wednesday.
AFP news agency quotes medical and military sources as saying at least 139 fighters – most of them rebels – have been killed. Houthi news sources say more than 50 pro-government forces have been killed.
The government has said it will not attack the port and will seek to preserve key infrastructure.
Meanwhile UAE military sources say a major force made up of Yemeni, UAE and Sudanese troops is on standby in Eritrea to take part in a final effort to capture Hudaydah.
Yemen has been devastated by a conflict that escalated in early 2015, when the Houthis seized control of much of the west of the country, including the capital Sanaa, and forced President Abdrabbuh Mansour Hadi to flee abroad.
Alarmed by the rise of a group they saw as an Iranian proxy, Saudi Arabia and eight other Arab states intervened in an attempt to restore Mr Hadi’s government.
Learn more about Yemen’s war
Almost 10,000 people – two-thirds of them civilians – have been killed and 55,000 others injured in the fighting, according to the United Nations.
The conflict and a partial blockade by the coalition have also left 22 million people in need of humanitarian aid, created the world’s largest food emergency, and led to a cholera outbreak that is thought to have killed 2,290 people.
The International Committee of the Red Cross (ICRC) has said it expects tens of thousands of people to flee Hudaydah in the coming days. Those who plan to stay have been stocking up on food and fuel in anticipation of a siege, it says.
In addition to being one of Yemen’s most densely populated areas, with an estimated population of 600,000, Hudaydah is the single most important point of entry in Yemen for the food and basic supplies needed to prevent a famine.
The UN has warned that in a worst-case scenario, the battle for the city could cost up to 250,000 lives, as well as cut off aid supplies to millions of people elsewhere.