President Abd-Rabbu Mansour Hadi was evacuated on Thursday after the planes opened fire, hitting his residence in the southern city.
"President Hadi has been evacuated to a safe place but he has not left the country," Hadi's aide told the AFP news agency as a plane made a second pass over the palace.
The aircraft dropped a bomb or fired a missile at the compound in al-Maasheeq district of the southern port city, where Hadi is based, the official said, in a sharp escalation of Yemen's months-long armed turmoil.
Residents said anti-aircraft guns opened fire at the planes, and smoke was seen rising from the area, but it was not immediately clear if Hadi was in the compound.
A Yemeni security source said the situation at the presidential palace "was under control and there was nothing to be worried about".
The attack on Hadi's compound came after forces loyal to Yemen's former president forced the closure of Aden's international airport after clashes left at least thirteen people dead and 13 wounded, security sources said.
A special forces unit, led by renegade General Abdel Hafez al-Saqqaf, stormed the airport grounds on Thursday before being repelled by fighters linked to the current president, Abd-Rabbu Mansour Hadi.
A military source told the AFP news agency that "Saqqaf's troops were forced to retreat to their camp [north of the airport] after being subjected to heavy shelling."