The coalition forces, which began the offensive on Wednesday, claim that arms are delivered to the Houthis through the port.
Military sources told dpa the coalition had launched several airstrikes on the southern outskirts of Hodeida, where agricultural areas have been turned into military bases by the rebels.
The sources, which are aligned with the Yemeni government, said the airstrikes are taking place alongside a ground offensive by the army.
The Red Sea port city has been under the control of Houthi rebels since 2014, when the Iran-allied group took over Sana'a and other parts of the country.
Seizing Hodeida would give the government forces and their allies an advantage over the Houthis, cutting a major route of supplies for the rebels and keeping them in mostly land-locked areas.
The devastating conflict intensified in March 2015, when the Houthis advanced on the southern city of Aden, which became the temporary seat of the government.
The move prompted Saudi Arabia and its Sunni allies to start an air campaign to push back the Shiite group.
Wednesday's offensive comes after the Saudi-backed Yemeni government said it would “move to restore legitimacy to the entire national territory after exhausting all peaceful and political means to force the Houthi militia out of the port of Hodeida."
Yemeni forces have been advancing towards the city for a few weeks.
Witnesses said the rebels had intensified their presence in the centre of the city and added extra military posts.
“Around 100 families have fled the outskirts of the city over the past few days to escape strikes and clashes,” said Manal al-Wasabi, an activist in Hodeida, adding that some families walked over six kilometres towards the city centre after Houthis demanded they leave their houses.
“Until now there are no shelters for them, so families have been separated, host communities have taken women in, while men were taken to an area in Hodeida airport, which is not very safe,” she added.
The operation to retake Hodeida will lead to "further escalation and instability" and have "devastating consequences" for civilians, top EU officials warned.
"An attack on the port of Hodeida, which is a critical facility for the delivery of life-saving items to the Yemeni population, would further deteriorate the already catastrophic humanitarian situation in the country," EU foreign policy chief Federica Mogherini and European Humanitarian Aid Commissioner Christos Stylianides said in a statement.
UN special envoy Martin Griffiths expressed concern that the military developments would hinder any chance of reaching an inclusive peace settlement through talks.
“I cannot overemphasize that there is no military solution to the conflict,” he said in a statement. “The United Nations is determined to move ahead with the political process despite the recent developments.”
In New York, the UN Security Council scheduled a last-minute meeting for Thursday at the request of Britain to discuss the offensive behind closed doors, diplomats told dpa.
The UN is continuing to offer humanitarian aid to those in need in Hodeida and the surrounding areas, despite reducing the number of staff due to security concerns ahead of the battle.
The UN rotated around a dozen international aid workers out and 41 national aid workers are still there, Dujarric told reporters in New York.
The International Committee of the Red Cross (ICRC) also pulled out some staff days ahead of the offensive due to security concerns.
The UN's team on the ground are providing 70,000 rapid-response kits - which include food rations for a family for two weeks - in Hodeida city and nearby areas, UN spokesman Stephane Dujarric said.
On Wednesday, the non-profit group Save the Children said there are around 300,000 kids in Hodeida city who are at risk of being killed or maimed by the fighting.
The ICRC said that the port and Sana'a airport were “lifelines to the outside world” and must be maintained.
Military sources told dpa the coalition had launched several airstrikes on the southern outskirts of Hodeida, where agricultural areas have been turned into military bases by the rebels.
The sources, which are aligned with the Yemeni government, said the airstrikes are taking place alongside a ground offensive by the army.
The Red Sea port city has been under the control of Houthi rebels since 2014, when the Iran-allied group took over Sana'a and other parts of the country.
Seizing Hodeida would give the government forces and their allies an advantage over the Houthis, cutting a major route of supplies for the rebels and keeping them in mostly land-locked areas.
The devastating conflict intensified in March 2015, when the Houthis advanced on the southern city of Aden, which became the temporary seat of the government.
The move prompted Saudi Arabia and its Sunni allies to start an air campaign to push back the Shiite group.
Wednesday's offensive comes after the Saudi-backed Yemeni government said it would “move to restore legitimacy to the entire national territory after exhausting all peaceful and political means to force the Houthi militia out of the port of Hodeida."
Yemeni forces have been advancing towards the city for a few weeks.
Witnesses said the rebels had intensified their presence in the centre of the city and added extra military posts.
“Around 100 families have fled the outskirts of the city over the past few days to escape strikes and clashes,” said Manal al-Wasabi, an activist in Hodeida, adding that some families walked over six kilometres towards the city centre after Houthis demanded they leave their houses.
“Until now there are no shelters for them, so families have been separated, host communities have taken women in, while men were taken to an area in Hodeida airport, which is not very safe,” she added.
The operation to retake Hodeida will lead to "further escalation and instability" and have "devastating consequences" for civilians, top EU officials warned.
"An attack on the port of Hodeida, which is a critical facility for the delivery of life-saving items to the Yemeni population, would further deteriorate the already catastrophic humanitarian situation in the country," EU foreign policy chief Federica Mogherini and European Humanitarian Aid Commissioner Christos Stylianides said in a statement.
UN special envoy Martin Griffiths expressed concern that the military developments would hinder any chance of reaching an inclusive peace settlement through talks.
“I cannot overemphasize that there is no military solution to the conflict,” he said in a statement. “The United Nations is determined to move ahead with the political process despite the recent developments.”
In New York, the UN Security Council scheduled a last-minute meeting for Thursday at the request of Britain to discuss the offensive behind closed doors, diplomats told dpa.
The UN is continuing to offer humanitarian aid to those in need in Hodeida and the surrounding areas, despite reducing the number of staff due to security concerns ahead of the battle.
The UN rotated around a dozen international aid workers out and 41 national aid workers are still there, Dujarric told reporters in New York.
The International Committee of the Red Cross (ICRC) also pulled out some staff days ahead of the offensive due to security concerns.
The UN's team on the ground are providing 70,000 rapid-response kits - which include food rations for a family for two weeks - in Hodeida city and nearby areas, UN spokesman Stephane Dujarric said.
On Wednesday, the non-profit group Save the Children said there are around 300,000 kids in Hodeida city who are at risk of being killed or maimed by the fighting.
The ICRC said that the port and Sana'a airport were “lifelines to the outside world” and must be maintained.