Yemen’s humanitarian situation has worsened rapidly since UN peace talks collapsed and fighting resumed in the port city of Hodeida, where hundreds of thousands of lives hang in the balance, the top UN aid official in the country has said.

“The situation has deteriorated dramatically in the past few days. Families are absolutely terrified by the bombardment, shelling and airstrikes,” the UN humanitarian coordinator Lise Grande said in a statement.

On Thursday, the Saudi-led military coalition attacking Houthi rebels seized the main road into the strategic port city of Hodeida, weakening Houthi control over the supply of humanitarian aid into the country.

“The mills in Hodeida feed millions of people,” Grande said. “We’re particularly worried about the Red Sea mill, which currently has 45,000 metric tonnes of food inside, enough to feed 3.5 million people for a month. If the mills are damaged or disrupted, the human cost will be incalculable,” she said.

The coalition restarted its offensive on the city at the weekend after UN-sponsored talks in Geneva failed to get off the ground last week. The Houthis claimed they had not been given adequate assurances about their travel to Geneva.

It is not clear whether the military coalition, which includes Saudi, Emirati and local Yemeni forces, plans to try to enter the city itself, where more than 300,000 people live.

“The main entrance in Hodeida leading to [the capital] Sana’a has been closed after forces backed by the [United Arab Emirates] took control of the road,” the coalition said in a statement.

It said more than 15 Houthis were killed in the operation, and its forces would now move to cut off the last road linking Hodeida to Sana’a, the Salih road to the north.

The fighting is being led by the Southern al-Amalka 3rd Brigade, commanded by Hamdi Shukri Alsubaihi.

The capture of the main road and surrounding area, at a minimum, increases the coalition’s ability to lay siege to the city, but it could also move to capture the port itself, more than 25 miles (40km) to the north of the city, and so avoid the main populated areas.

The Saudis argue the port is used by Iranian-backed Houthis as a way of extracting revenue and smuggling arms.

On Wednesday, the US secretary of state, Mike Pompeo, brushed aside claims that the Saudi bombing campaign was breaching international humanitarian law, and instead certified arms exports to Saudi could continue.

The US state department said the Saudis were taking demonstrable actions to protect civilian lives. Pompeo was forced to make the endorsement after Congress required him by law to examine whether the Saudis were following the rules of war.

The state department added: “The Trump administration has been clear that ending the conflict in Yemen is a national security priority. We will continue to work closely with the Saudi-led coalition to ensure Saudi Arabia and the UAE maintain support for UN-led efforts to end the civil war in Yemen, allow unimpeded access for the delivery of commercial and humanitarian support through as many avenues as possible, and undertake actions that mitigate the impact of the conflict on civilians and civilian infrastructure.”

The endorsement is likely to be seen as a green light for the Saudi coalition to press ahead with its assault on the Iranian-backed Houthis. Writing for the Washington Post, Yousef al-Otaiba, the UAE ambassador to the US, portrayed the war as a battle to defeat Iran and al-Qaida, adding that Qatar had been backing al-Qaida-linked forces. Qatar had made counter-allegations in the same newspaper.

A debate in the UK’s House of Commons on Wednesday revealed Conservative MPs were deeply divided over Saudi tactics, and the damage being inflicted on the reputation of the Gulf States due to the war.