Forces loyal to exiled President Abd-Rabbu Mansour Hadi also took Aden's central district of Khormaksar, and aid sources reported fighting around the port area.
Backed by air support from a Saudi-led coalition, the loyalist forces launched a wide-ranging assault in Aden this week to reclaim territory held by the Iranian-allied Houthis.
"Aden International Airport and Khormaksar have been cleared of Houthi and Saleh elements by armed forces backing Yemen's legitimacy and the popular resistance forces, in coordination with and with direct support by the coalition," Yemeni government spokesperson Rajeh Badi said.
He said he expected Aden to be cleared completely within the coming days.
A coalition of Arab states has been bombarding Houhti forces, Yemen's dominant power, since late March in a bid to reinstate Hadi.
He was ousted from the power when the Houthis took over the capital Sanaa in September then fled to Riyadh as Houthi forces closed in on Aden, where he had sought refuge.
A UN-brokered ceasefire to allow delivery of aid to a city desparately short of food, medicine and other necessities collapsed on Monday after Saudi Arabia said it did not recognize the truce and continued air strikes.
Read: Saudia-led strikes hit Yemen rebels despite truce
"The fighting in Aden began in the morning as the forces approached Aden from different positions," said Ali al-Ahmadi, spokesperson for the Southern Popular Resistance, which is defeding Aden from the Houthis.
"After violent clashes that continued for hours the forces were able to enter the airport and Badr base and they killed a large number of the militias."
On the humanitarian front, the UN' World Health Organization managed to deliver medical supplies to Aden but it said food rations have been delayed.
"It took us days and days and days to organise the safe passage...But it did arrive in Aden last Saturday. It was the first time that we got a convoy into Aden for weeks," Johannes Van Der Klaauw, the UN humanitarian coordinator for Yemen, said in Geneva.
The UN World Food Programme said a 40-truck convoy carrying enough food to feed 117,000 people for a month had reached Aden province after being held at a checkpoint for days.
But hopes of shipping 500,000 litres of fuel to Aden were still stymied by security problems.
"The area around the port for the last 48 hours has been a war zone," WFP spokesperson Abeer Etefa said.
More than 3,000 people have been killed and more than one million displaced since the conflict broke out.
Yemen had been in the frontline of the United States's global war against militants but American personnel pulled out of the country as the internal conflict worsened.
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