The clash coincided with a drone attack that killed three suspected Al-Qaeda militants in southern Yemen, tribal sources said.
An official in the southern province of Lahij said the separatists opened fire on an army convoy and three soldiers were wounded in a gunbattle.
The separatists last week abducted 12 soldiers and threatened to kill them unless the army handed over a military base to offset the growing influence of the Shiite Huthi militia that has seized Sanaa.
Hadi escaped last week to Aden, where he has been reconsolidating his grip on power buoyed by support from Gulf states which have relocated their embassies to the southern city.
Several countries, including Britain and the United States, closed their embassies in Sanaa over security fears following the Huthi takeover.
Hadi's escape to Aden has turned what was the capital of an independent south Yemen before unification in 1990 into a diplomatic hub.
"We have suspended our participation in the (UN-backed) national dialogue until it is moved out of the country," Southern Movement member Yassin Mekkawi said.
He said negotiators were facing mounting "political and psychological pressure".
UN envoy Jamal Benomar has been shuttling between Yemeni parties to secure an end to the country's political deadlock and to persuade them to return to the negotiating table in Sanaa.
But there has been widespread disagreement on the venue.
Ousted president Ali Abdullah Saleh's party, however, insists the talks resume in Sanaa, warning of a boycott.