Saudi-backed coalition forces ratcheted up their assault on the key port city of Hodeidah in Yemen on Friday as the U.N. and human rights organizations warn that the “worst humanitarian crisis in the world” is about to get much worse.

The battle for Hodeidah, a rebel-held port city on the western coast of the war-ravaged country, entered its third day on Friday, with a Saudi-led coalition continuing to pound targets along the coast with airstrikes, while troops loyal to the exiled government amassed on the city’s southern side.

The forces, led by the United Arab Emirates, were within meters of capturing the airport in Hodeidah on Friday, according to Saudi-owned television station Al Arabiya.

As residents of the city were marking the end of Ramadan by gathering at dawn in an open area for Eid al-Fitr prayers, one resident told Reuters: “Many warplanes were flying low over the city during the prayers.”

The Western-backed coalition forces also sought to prevent the Iran-backed Houthi rebels from calling in reinforcements from the capital Sanaa by hitting the main road between the two cities.

The coalition forces believe the capture of Hodeidah would give them the upper hand in a war that has seen neither side make any real advances in years, despite more than 10,000 people being killed.

The U.N. says it is struggling to ensure that Hodeidah remains open to aid shipments, with the port said to account for up to 80 percent of the humanitarian supplies that enter the country.

A direct strike on Hodeidah’s port by the coalition would significantly hurt the rebels’ chances of holding onto control of the city, but the coalition is equally aware that such a strike would lead to a significant international backlash — even from the U.S., which is currently providing logistics and training support to the coalition.

A Saudi blockade of the country, imposed after Houthis fired a missile at its capital Riyadh, has put tens of millions of people at risk of starvation, in a country that relies heavily on imports for food, fuel, and medicine.

“I urge all parties to the conflict to meet their obligations to protect civilians and civilian infrastructure and take active steps to respect international humanitarian law,” David Beasleye, executive director of the U.N. World Food Programme, said in a statement.

Human Rights Watch says both sides are “bound under the laws of war” to minimize civilian casualties, but it points out that both the Houthis and coalition forces have already shown scant regard for such rules.

“The coalition and Houthi forces now fighting for Hodeidah have atrocious records abiding by the laws of war,” Sarah Leah Whitson, Middle East director at Human Rights Watch, said Friday. “The U.N. Security Council should urgently warn senior officials on both sides to provide civilians access to desperately needed aid.”

The U.N. has labeled Yemen the “worst humanitarian crisis in the world” and the World Health Organization says that more than 8 million people are living in pre-famine conditions.

On Thursday, during a closed-door session of the U.N. Security Council, members expressed their “deep concern about the risks to the humanitarian situation,” but they dismissed a call by Sweden to freeze the military operation to allow time for talks on a rebel withdrawal from the Red Sea port.

On Thursday evening, exiled Yemeni President Abd Rabbu Mansour Hadi arrived in Aden, the temporary capital of the war-wrenched country, saying: “The hour of victory is close and the return of justice is nearing that will lead to the triumph of the will of the Yemeni people.”

Speaking on Twitter Friday morning, Minister of State for Foreign Affairs Anwar Gargash, said: “Depriving the Houthis of their control of Hodeida port, at the Yemeni government request, means that the Houthis will no longer be able to impose their will at the barrel of a gun.”

In the U.S., Democratic Rep. Adam Schiff called on the White House to do more to secure the safety of those living in Yemen.