Residents identified them as Ansar al-Sharia, a local affiliate of al Qaeda.
At least seven local militiamen and five militants were killed, according to local fighters. Militants were deployed to the streets of both towns, and in Jaar blew up the house of a local commander killed in the fighting, residents said. Schools and shops were closed.
Later on Wednesday, a clinic in the southern city of Taiz run by Medecins Sans Frontieres (MSF) was hit by airstrikes by a Saudi-led coalition, the medical aid group said.
The Saudi-led coalition since March has been trying to defeat Yemen`s Iran-backed Shi`ite Houthis, who captured large parts of the country and wrested control from its government, which only recently returned from exile.
"The entrance of al Qaeda this time happened in the absence of any state institutions, which al Qaeda exploited," said Zinjibar resident Fadl Mohammed Mubarak.
Jaar and Zinjibar are about 50 km (30 miles) east of the main port city of Aden, where President Abd-Rabbu Mansour Hadi is staying after returning from Saudi Arabia last month.
Parts of Abyan including Zinjibar and Jaar fell to Islamist militants in 2011 for over a year as government control waned during Arab Spring protests.
MOBILE CLINIC BOMBED
This time, Yemen`s northern Houthi clan and forces loyal to former president Ali Abdullah Saleh are fighting against the Saudi-led Arab coalition and fighters loyal to Hadi.
MSF said in a statement on Wednesday that seven people had been wounded, two critically, when airstrikes carried out by the Saudi-led coalition destroyed a mobile clinic in Taiz where it provides medical care.
U.N. Secretary-General Ban Ki-moon condemned the bombing of the clinic, his press office said in a statement.
"(Ban) underscores that medical facilities and medical personnel are explicitly protected under international humanitarian law," it said. "He calls for a prompt, effective and impartial investigation into today`s incident."
A Saudi coalition spokesperson was not immediately available to comment.
Hospitals have come under attack in the flashpoint city of Taiz, which in recent months has been besieged by Houthi fighters and bombarded by Saudi fighter jets.
On Oct. 27, a hospital in north Yemen, also run by MSF, was destroyed by a missile strike that MSF said was launched by the Arab coalition. Saudi Arabia denies its planes hit the hospital.
NO HELP DESPITE WARNING TO GOVERNMENT
In Abyan, local militia commander Abdullatif al-Sayed said his forces tried to repel the morning attack by al Qaeda.
He said he had tried to alert government officials to apparently suspicious al Qaeda movements, but got no help.
Fighters allied with Hadi, backed by the Saudi-led coalition, retook Aden from the Houthis in July, but residents have complained of lawlessness in the city as masked Islamist gunmen appeared on its streets.
Jaar has in past years lost civilians in airstrikes intended for militants and, during a visit by Reuters to Jaar in late 2013, sympathy for militants was still evident.
Tribal leaders have often warned U.S. drone attacks on al Qaeda were creating sympathy for the group.
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