CARE International, one of the few aid agencies still there, said 30 airstrikes hit the city within half an hour.
The UN Security Council is expected to meet to discuss the situation on Thursday, following a request from the UK. They spoke on condition of anonymity as they weren't authorised to brief journalists.
UAE Minister of State for International Cooperation Reem al-Hashimy said if the port was no longer under Houthi control then the coalition could ease controls aimed at denying arms to the group by doing away with inspections at the Saudi port of Jizan.
"The liberation of Hodeidah port is a turning point in our struggle to recapture Yemen from the militias that hijacked it to serve foreign agendas", the exiled government said in a statement carried by state-run Yemeni media. But the first wave of this relatively high-tech assault by irregular Houthi forces occurred back on October 2nd, 2016 when the high-speed logistics catamaran HSV-2 Swift was destroyed by an anti-ship missile.
It added that the attacking forces managed to "liberate areas.in the surroundings of the airport" and captured and killed "dozens of Houthi" rebels.
The Red Sea port is the only port under Houthi control, situated about 150km southwest of the capital, Sanaa. Worldwide observers have warned that a military fight over the port city could halt life-saving food and medicine and cause the starvation of millions. There was no immediate confirmation from the coalition.
The fear is that a protracted fight could force a shutdown of Hodeida's port at a time when a halt in aid risks tipping millions into starvation.
On Tuesday, the exiled government said its forces and allied Saudi-led troops launched their assault after "exhausting all peaceful and political means".
The UN on Monday withdrew all of its worldwide staff from Hodeida ahead of the impending assault, warning that any offensive would put millions of lives at risk. Lasting peace and stability in Yemen will require dialogue and negotiation.
Riyadh says the Houthis use the port to smuggle Iranian-made weapons, including missiles that have targeted Saudi cities - accusations denied by the group and Iran.
"All member states, led by the US, must demand that vital humanitarian and commercial imports through Hodeidah are maintained", said David Miliband, head of the International Rescue Committee. The sound of heavy, sustained gunfire clearly could be heard.
The Security Council has strongly supported efforts by new United Nations special envoy Martin Griffiths to resume political negotiations and avoid a military escalation of the three-year-long conflict that has killed more than 10,000 people, displaced more than 2 million, and created the world's worst humanitarian crisis.
"As many as 250,000 people may lose everything - even their lives", the United Nations said.
"It is extremely important that hospitals be spared, that civilians be spared, and that those who might want to flee Hodeidah because of the fighting be allowed to do so safely", the ICRC spokeswoman told RT. "This is possibly what we're most concerned about".
The new United Nations envoy to Yemen, Martin Griffiths, tweeted that he was "extremely concerned" by the violence, calling on all parties to exercise restraint.
Today marked a watershed moment in the Yemeni conflict; a day the Saudi-led coalition has sought to avoid but had become impossible to delay for the sake of the Yemeni people. The U.S. has been offering targeting information to the Saudi-led coalition, as well as refuelling their warplanes, though its role in Wednesday's assault wasn't immediately clear.