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. BBC said
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.