"Liberation of the port of Hodeidah is a milestone in our struggle to regain Yemen from the militias".
"It will secure navigation in the Bab al-Mandab Strait and cut off the hands of Iran".
Houthi-run Al Masirah TV said two missiles struck the barge, but there was no immediate confirmation from the coalition.
"Such hostile acts by the Iran-backed Houthi militias prove the continuing involvement of the Iranian regime in supporting the Houthi militias with qualitative capabilities in a flagrant and explicit violation of the two United Nations resolutions No. 2216 and 2231 with the objective of threatening the security of the Kingdom of Saudi Arabia as well as the regional and global stability", the spokesman said.
UAE's Minister of State for Foreign Affairs Anwar Gargash earlier told French newspaper Le Figaro the deadline for a withdrawal from Al Hodeida by the Houthis expired early on Wednesday morning.
Explosions were heard on the outskirts of the port city, it added.
UN Secretary-General Antonio Guterres had said that UN envoy Martin Griffiths was in "intense negotiations" in an attempt to avoid a military confrontation. The port is 150km (90 miles) south-west of Sanaa, Yemen's capital held by the Houthis since they swept into the city in September 2014.
The UN and International Committee of the Red Cross said on Wednesday that all parties in Yemen's war must protect civilians.
"Under worldwide humanitarian law, parties to the conflict have to do everything possible to protect civilians and ensure they have access to the assistance they need to survive", Lise Grande, U.N. humanitarian coordinator for Yemen, told Reuters by email.
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 Hudaida port is crucial for the flow of food supplies into a country that is on the brink of starvation.
Abu Dhabi's critics say the UAE military operations have focused on port cities to control commerce in the strategic region, not to drive out the Houthis.
"I think the Emiratis have done a good job in presenting compelling arguments about why an operation (on Hodeidah) could in the end tip the balance and apply enough pressure to bring the Houthis to the table", a Western diplomat said on Monday.
Hodeidah is the lifeline for the majority of Yemen's population, who live in Houthi territory.
"The Yemeni government and the coalition have accepted the proposal".
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 Saudi-led coalition did not immediately acknowledge the incident.