Under the control of al-Qaida militants since 2011, Jaar was declared an Islamic Caliphate by the militants in March 2012.
Violent clashes in the outskirts of Jaar broke out on Friday evening, the al-Ghomoriya newspaper reported.
Five Islamist fighters were killed in the fighting on Friday, putting the death toll at a reported 116 al-Qaida fighters since last Saturday, the Aden Times reported.
In Mukallah, a city situated in the eastern province of Hadramaut, security officers told al-Ghomoriya that gunmen allegedly linked to al-Qaida had tried to infiltrate the city at night.
The Defense Ministry said all southern provinces were now on alert.