Hadi was forced to evacuate the palace in the country's major southern city, presidency sources said, after it was attacked by a fighter jet.
The same sources claimed that the attack was repelled by anti-aircraft guns stationed near the palace, where Hadi was at the time, forcing the plane to retreat.
"President Hadi has been evacuated to a safe place but he has not left the country," the source told AFP as the plane made a second pass over the palace.
Hadi took refuge in Aden last month after fleeing house arrest under the Huthi militia that has taken control of the capital Sanaa.
The targeting of the palace came just hours after deadly clashes forced the closure of Aden's international airport.
At least six people were killed and 20 wounded after fierce fighting broke out between Hadi supporters and opponents, security sources said.
The clashes erupted between a special forces unit loyal to the Shiite Huthi militia, who since last year have seized large parts of central Yemen, and pro-Hadi paramilitary fighters, security sources said.
The special forces fighting at the airport were led by renegade General Abdel Hafez al-Saqqaf and met heavy resistance from fighters with the Popular Committees, a local paramilitary group that backs Hadi.
Several hundred soldiers loyal to Hadi -- supported by tanks and armoured vehicles -- were also dispatched as reinforcements to the airport.
Three members of the special forces were killed along with two from the Popular Committees, sources said. Another special forces member was killed in separate fighting in central Aden.
Yemen, a key US ally in the fight against al-Qaeda, has been gripped by unrest since ex-strongman Ali Abdullah Saleh stepped down in early 2012 after a year-long popular uprising against his rule.
Saleh -- along with Iran -- has been accused of backing the Huthis, who took control of Sanaa in September and earlier this year seized key government buildings in the capital.
