Fighting has intensified around the largest hospital operating in the port city of Hodeidah, preventing access to severely malnourished and vulnerable children, the UN’s children’s agency has warned.

The escalation in conflict follows US calls for a ceasefire and suggestions that peace talks may be held in Sweden. On Thursday, the Saudi-led coalition said it had attacked Sana’a international airport and an adjoining airbase being used by Houthi insurgents.

“It’s very clear that, despite the call for talks, and despite the call for an agreement on the cessation of hostilities in the next 30 days, the parties are intensifying the fighting – unfortunately, with an incredible impact on children,” said Geert Cappelaere, Unicef’s regional director for the Middle East and north Africa, speaking from Sana’a.

Cappelaere said the few shipments of crucial medical supplies and food arriving in the port of Hodeidah were regularly blocked, sometimes for months. “Even the humanitarian aid is taken hostage at times. It’s just unacceptable. All parties are carrying responsibility,” said Cappelaere. “The war on children needs to stop.”

Active fighting is taking place within a few hundred metres of the largest of Hodeidah’s handful of hospitals, according to Cappelaere, who visited the city this week. Families were delaying seeking medical attention because of the hostilities, or because they could not afford the transport costs.

Hodeidah, which has been hit particularly hard by cholera and acute diarrhoea, was already among the worst places for children in Yemen, Cappelaere said.

The latest Unicef figures show there are an estimated 1.8 million malnourished children in Yemen. Almost 400,000 children are suffering from severe acute malnutrition, which is life-threatening, with four in 10 of such cases in Hodeidah and neighbouring governorates.

On a visit to Al-Thawra hospital, Cappelaere said he saw the emaciated bodies of acutely malnourished children, as well as several children paralysed by diphtheria, which is preventable by vaccine. Among them was a 10-year-old girl, Sara, who is paralysed from the chest downwards because of the infection.

“I was just thinking overnight when I heard the shelling happening … What does that mean for that poor girl who is already half-paralysed and who now has to hear all these bombs around her? For what reason? To get a better negotiating position around the table in Sweden?” said Cappelaere.

It is feared that intensified fighting in Hodeidah would not only have a devastating impact on its population but also cut off food, fuel and medical imports to the rest of the country. Aid agencies have repeatedly warned the conflict is driving Yemen to the brink of the worst famine in living memory.

The UN under-secretary general for humanitarian affairs, Mark Lowcock, said last week that if fighting continues, famine could engulf the country within three months, with 12 to 13 million people at risk of starvation.

The US defence secretary, James Mattis, said on 31 October that Saudi Arabia and its Emirati allies were ready for a deal, and that the talks between the Saudi-led coalition and the Houthi rebels were being arranged by the UN special envoy for Yemen, Martin Griffiths.

Government forces patrol as smoke billows from an alleged Houthi position during fighting in the port city of Hodeidah. Photograph: Najeeb Almahboobi/EPA

An all-out offensive on Hodeidah city or port before the talks “would have severe consequences” said Frank McManus, Yemen country director for the International Rescue Committee (IRC).

“Any party launching an attack on the city/port at this time would be hard pressed to convince the international community that such a move was not designed to scuttle the peace process,” McManus said.

A UN report due in mid-November will determine how close Yemen is to famine. Recent screening conducted by the IRC in a village in Bayt al-Faqih of Hodeidah governorate found that just under 15% of children were malnourished. Of 2,839 children screened at random by the charity, 384 were either moderately or severely malnourished.

At a hospital in a nearby town of 72,000 people, there are 50 new cases of malnourished children each day, on average. Of these, 15 are severely malnourished.

While fighting is preventing shipments from arriving in the country, the currency has collapsed in value, leaving people unable to afford food, which has nearly doubled in price.

Cappelaere said parties to the conflict, and those supporting them, must put children’s interests first. “We need parties to enable us to do our work without any hindrance, and we need donors who are generous to continue to be generous,” he said.