The battle over the Yemeni port of Hudaydah has intensified as government forces backed by the coalition's Saudi Arabian air strikes advance to rebel positions.
More than 150 people have reportedly been killed since troops and militia officers launched a ground attack on the city's outskirts last Thursday.
The United Nations and charities say the fighting is also jeopardizing medical facilities and hundreds of thousands of civilians.
The port of Hudaydah is a lifeline to millions of Yemenis threatened by starvation.
Up to 80% of the humanitarian supplies, fuel and merchandise they rely on are supplied by the institution, and United Nations officials have warned that the death toll could be catastrophic if damaged, destroyed or blocked.
Yemen was devastated by a conflict that escalated in 2015 when the Arab states intervened after the rebellious Houthi movement seized control of most of the country's west and forced President Abdrabbuh Mansour Hadi to flee overseas.
According to the United Nations, at least 6,660 civilians were killed and 10,560 injured during the war. The fighting and a partial blockade by the coalition have also resulted in 22 million people needing humanitarian aid, creating the world's largest food security emergency, leading to an outbreak of cholera that affected 1.1 million people.
The offensive in Hudaydah, led by the United Arab Emirates, began in June.
Government soldiers and militia officers made rapid progress at first, conquering the southern suburbs of the city and the airport. But they did not penetrate downtown, where rebels position fighters, dig ditches in streets, and land mines.
The escalation of fighting last week came after the US – which is logistically and intelligently supporting the coalition along with Great Britain and France – called for the cessation of hostilities and the beginning of peace talks by the end of November.
On Saturday alone, 200 airstrikes were reported in a round-trip flight around Hudaydah, and aides say there were fierce clashes around the airport in the east of the city and near a university in the west.
On Wednesday, Save the Children said a Hudaydah-backed health facility had been attackedDamaging a pharmacy that supplies much needed medication.
Artillery shells also hit residential areas, and temporary roadblocks prevented people from leaving or entering the city overnight, which actually included them in an active conflict zone.
The United Nations Children's Fund (Unicef) warned on Tuesday that the fighting was "dangerous" near the Al-Thawra Hospital in southern Hudaydah. The lives of 59 children, including 25 in the intensive care unit, are in mortal danger.
"The medical staff and patients in the hospital have confirmed they hear heavy bombing and gunfire, and access to and from the hospital, the only functioning hospital, is now in jeopardy," said CEO Henrietta Fore.
"In particular, children can not afford Al-Thawra to be involved in the fighting, and Hudaydah and neighboring governments account for 40% of the country's 400,000 children suffering from severe acute malnutrition, and some are taken to the hospital for emergency treatment Caring, "she added.
The International Committee for the Red Cross (ICRC) also expressed its concern over the fighting near the Al-Thawra Hospital and called on all parties to respect international humanitarian law and to protect civilians and civilian infrastructure.
Previously, there were unconfirmed reports that Houthi fighters had been stationed in or near medical facilities to evidently avoid coalition and artillery strikes.
One resident told the Guardian newspaper that rebels had raided the hospital on Tuesday, May 22, north of the main road to the capital, Sana'a, and set up sniper positions on their roof.
The Houthi-led Ministry of Human Rights accuses the coalition of targeting grain silos in Hudaydah, where tens of thousands of tons of wheat and flour and local roads, bridges, factories and markets are stored.
The coalition said it had no plans to invade Hudaydah's city or port, but its forces could try to surround it and lay siege before UN Special Envoy Martin Griffiths resumes the peace talks.
The coalition has accused the Houthis of using Hudaydah to smuggle weapons from their ally Iran. That is what both Iran and the rebels have denied.