Yemeni forces recaptured Aden's international airport and some city districts from Houthi militia fighters on Tuesday, in a sudden advance after months of stalemate, the exiled government said.

Yemenis on social media reported celebrations in cities across the country's south, where refugees from Aden have fled, and in other areas where local fighters are still battling the Houthis and army units loyal to former president Ali Abdullah Saleh.

Houthi-run Maseera television reported that the Houthis had chosen to quit the city after "cleansing it of al Qaeda and Islamic State" in an apparent admission of the militia's retreat.

Photographs on southern Yemeni media, which Reuters could not immediately verify, appeared to show a column of armoured vehicles advancing along a street in Aden, where the fighting has mostly involved guerrilla fighters in civilian clothes.

The fighting followed the collapse of a humanitarian truce brokered by the United Nations.

Local fighters aligned with exiled President Abd-Rabbu Mansour Hadi took control of 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 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 spokesman Rajeh Badi said.

He said he expected Aden to be cleared completely within the coming days.

A coalition of Arab states has been bombarding Houthi forces, Yemen's dominant power, since late March in a bid to reinstate Hadi. It has also run training programmes for Yemeni soldiers loyal to Hadi and dropped arms to local forces fighting the Houthis.

Hadi was ousted from power when the Houthis took over the capital Sanaa in September. He then fled to Riyadh as Houthi forces closed in on Aden, where he had sought refuge.

A U.N.-brokered ceasefire to allow delivery of aid to a city desperately short of food, medicine and other necessities collapsed on Monday after Saudi Arabia said it did not recognise the truce and continued air strikes.

"The fighting in Aden began in the morning as the forces approached Aden from different positions," said Ali al-Ahmadi, spokesman for the Southern Popular Resistance, which is defending 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."

The U.N.'s World Health Organization managed to deliver medical supplies to Aden but it said food rations have been delayed. – Reuters