Coalition aircraft and ships pounded Houthi positions in the Yemeni city of Hodeidah for a second day on Thursday, as troops moved closer to capturing the airport.
The Arab-backed offensive included the use of Apache attack helicopters to hit a strip of coastal territory controlled by the Iran-backed rebels.
The coalition also struck the main road linking Hodeidah to the rebel-held capital Sanaa, which lies north-east, to block reinforcements, residents and Yemeni military officials said.
UAE Minister of State for Foreign Affairs Dr Anwar Gargash said the military operation, named Golden Victory, would open the way to a political process leading to peace in Yemen.
Of the Houthis, he said: "They overthrew the country's constitutional government and have oppressed and plundered the country since."
By Thursday evening, UAE and Saudi forces were two kilometres south of the city's airport, according to government officials, representing an advance of three kilometres from 24 hours earlier. The centre of the city of 600,000 people lies 4km further north, and the seaport several kilometres beyond that.
Two senior Houthi commanders were reported killed in fighting near the airport on Wednesday and Thursday. The clashes on Thursday left 30 Houthis dead, medical sources told the AFP news agency, with nine pro-government troops killed in the same area. Military sources said the deaths were caused by mines and snipers.
The clashes came as the UN Security Council prepared to hold urgent talks on the military operation.
The Arab coalition intervened in the war in 2015 at the request of the internationally-recognised government of Yemeni President Abdrabu Mansur Hadi.
The current offensive on Hodeidah is the first time since the coalition joined the war that they have attempted to capture such a well-defended city. Their aim is to box in the Houthis in the capital Sanaa, cut their supply lines and force them to the negotiating table.
"This deadlock must end," Dr Gargash said, adding that it is clear that for the UN-led political process to succeed, the situation on the ground must change.
On Thursday, Saudi Arabia's air defence forces shot down a missile over the town of Khamis Mushayt which had been fired from Yemen.
The Houthi militia has repeatedly fired missiles at Saudi Arabia, which the United States and UN experts say are of Iranian origin, a claim Tehran denies.
The UN and International Committee of the Red Cross have urged all parties in Yemen’s war to protect civilians.
Hodeidah's port handles 80 per cent of essential goods coming into Yemen, where 8.4 million people face pre-famine conditions, according to the World Health Organisation.
The coalition, however, says the Houthis have used the port not only to smuggle Iranian-supplied weapons into the country but also to profit from illegally sold humanitarian aid.
Yemen has been in crisis since the 2011 mass protests that ended then president Ali Abdullah Saleh's 33-year rule.
Mr Hadi came to power in a Saudi-brokered transition, but the Houthis drove him out. For a time Mr Saleh joined forces with the Houthis, but they turned on each other last year and the former president was killed. Parts of Yemen are also held by Al Qaeda and ISIS.
On Thursday, authorities said the Red Sea port remained open to shipping despite the nearby fighting.
"We still have seven ships in the port. The work in the port is normal. And we have five other ships standing by waiting outside to enter," said port director Dawood Fadel.
Saudi and UAE aid ships remain in waters west of Hodeidah, said coalition spokesman Turki Al Maliki.
Obaid Salem Al Zaabi, UAE ambassador to the United Nations in Geneva, meanwhile, said four Emirati troops killed in Yemen had been taking part in the campaign to retake Hodeidah.
The ambassador made the comments during a news conference with journalists in the Swiss city.
Abdullah Al Rabeeah, head of Saudi Arabia's King Salman Aid and Relief Centre, in a press conference late Wednesday sought to allay the fears of the international community over the coalition's military operations.
"This coalition will start to operate an air and sea bridge, as well as land, to transport aid and medical supplies, food, shelter and fuel other basic necessities to Hodeidah province," he told reporters.
Aides to President Hadi, who has spent much of the war in exile in Riyadh, said he was preparing on Thursday to visit the southern port city of Aden, where the government set up its base after it was forced out of Sanaa.
"President Abdrabu Mansur Hadi will arrive to the interim capital of Aden in the coming hours … from Saudi Arabia, along with a number of his advisers and senior officials," a senior Yemeni government source told AFP.
The United Nations pulled all of its international staff out of Hodeidah on Monday.
UN envoy to Yemen Martin Griffiths is due to present a peace plan to the Security Council next week.