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, the southern city's deputy governor Naef al-Bakri told AFP.
Bakri did not give details on the operations but said 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".
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"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 to AFP that they had sustained "heavy losses".
Aden health chief Al-Kheder Lassouar said at least 19 civilians and anti-rebel fighters have been killed in two days of fighting there.
Similar strikes on Fajj Attan last month set off a chain of explosions that killed 38 civilians.
Amnesty International warned today that "scores of casualties in Sanaa have been caused by anti-aircraft munitions shot by the Huthi armed group which detonated after landing in populated areas, killing and maiming civilians".
The London-based rights group's senior crisis adviser Lama Fakih said both the coalition and the rebels "have failed to take the necessary precautions to protect civilian lives in violation of the laws of war. Instead they have carried out attacks that have had devastating consequences for the civilian population."
"The Huthi armed group should also move its military positions away from populated civilian areas where feasible," the watchdog said.
Other strikes today hit the rebel stronghold of Saada in the country's north.
The Yemen conflict has killed almost 2,000 people and wounded 8,000, according to the World Health Organization.