Residents reported non-stop air raids on rebel positions across the city amid heavy fighting.
The coalition air campaign against the rebels and allied forces loyal to former leader Ali Abdullah Saleh began on March 26 in an effort to restore UN-backed President Abedrabbo Mansour Hadi to power.
"Coalition forces carried out qualitative and successful operations against the rebels after coordination between the coalition leadership and the Popular Resistance Council leadership" on the ground in Aden, says the southern city's deputy governor Naef al-Bakri.
Anti-rebel forces -- pro-government fighters, Sunni tribes, and southern separatists -- are referred to as Popular Resistance Committees.
Bakri did not give details on the operations but said that warplanes destroyed a number of rebel vehicles and hit checkpoints in Aden's north and northeast, adding that Popular Resistance fighters were also "provided with qualitative weapons".
"At least 40 rebels were killed and dozens were wounded" in air strikes and fighting, he said.
A military source close to the Huthis confirmed that they had sustained "heavy losses".
Aden's health chief al Kheder Lassouar said at least 19 civilians and anti-rebel fighters have been killed in two days of fighting there.
The Yemen conflict has killed almost 2,000 people killed and wounded 8,000, according to the World Health Organisation.
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