The clashes broke out last night and lasted for hours in a central area of the city, which caused panic among the population, reported the Al Ain news website.
According to the source, the fighting took place in the Suq al Thulath area between a militia known as the Stability Support Force and another self-called Public Security Force.
Both sides used medium and heavy weaponry, which damaged several properties, although no casualties are reported so far, the source said.
After a year of relative calm, fears of a new outbreak of violence have increased since early February, when parliament appointed Fahi Bashagha as interim prime minister to replace Abdul Hamid Dbeibeh, who refused to hand over power.
The nation has been in a spiral of violence since the overthrow of Muammar al-Gaddafi in 2011, following a war supported by members of the North Atlantic Treaty Organization, including the United States, France and the United Kingdom.