But it could set off a prolonged street-by-street battle that inflicts heavy casualties.
The Red Sea port is the main entry for food into a country already on the brink of starvation.
In reality, families in Hudaydah are already starving and desperately relying on humanitarian aid.
CARE International, one of the few aid agencies still there, said 30 air strikes hit the city within half an hour.
Aid groups have expressed grave concerns for the safety of hundreds of thousands of civilians in the city whose lives could be at risk from the assault launched Wednesday. "We thought it could not get any worse, but unfortunately we were wrong".
The initial battle plan appeared to involve a pincer movement.
"The liberation of Hudaydah 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 separate statement carried by state-run Yemeni media.
The Red Sea port, controlled by the Iran-backed Houthi rebels who hail from northern Yemen, serves as the entry point for 70% of the impoverished country's imports as it teeters on the brink of starvation.
A Yemeni anti-Houthi military official said the alliance had brought to bear a 21,000-strong force. There was no immediate confirmation from the coalition.More news: Prince Harry and Meghan Markle 'rent converted cowshed' in Cotswolds
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The sources said Yemeni forces allied to the Saudi-led coalition - drawn from southern separatists, local units from the Red Sea coastal plain and a battalion led by a nephew of late former president Ali Abdullah Saleh - had advanced and were "at the doors" of Hodeidah airport.
The United Nations and other aid groups already had pulled their worldwide staff from Hudaida ahead of the expected assault. Several ships arrived in recent days, including oil tankers, and there was no word from the coalition or the United Nations to stop work, according to a senior port official.
Aid groups nevertheless warned of disaster. An assault was "likely to exacerbate an already catastrophic humanitarian situation", Red Cross spokeswoman Marie-Claire Feghali said.
The UN and the International Committee of the Red Cross (ICRC) called on Wednesday for all sides to protect civilians.
The war in Yemen has displaced 2 million more and helped spawn a cholera epidemic. The Saudi-led coalition has been criticized for its airstrikes killing civilians.
The Red Sea port is the only port under rebel control and the coalition says Houthis are using it to smuggle weapons.
"Cutting off imports through Hodeida for any length of time will put Yemen's population at extreme, unjustifiable risk", Lise Grande, UN humanitarian coordinator for Yemen, said.
He said "aid operations will be severely challenged in the event of sustained fighting in densely populated urban areas" and stressed that people trying to flee conflict areas "must be allowed to do so without any hindrance". "We are also deeply concerned that these operations jeopardize prospects for a near-term political resolution to the conflict".
The possibility of food running out is also among the residents' main fears.
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. However, Griffiths' recent appointment as envoy and his push for new negotiations may have encouraged the Saudi-led coalition to strengthen its hand ahead of any peace talks with the Houthis.
The attack also comes as Washington has been focused on President Donald Trump's recent summit with North Korean leader Kim Jong Un. 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.