Gunmen were deployed throughout most of Aden's districts and there was heavy automatic gunfire and explosions in the southern port city, according to Reuters witnesses.
The southern port city of Aden is considered as Yemen's temporary capital and the Saudi-backed Yemeni government based itself there since 2015.
There have been rising tensions between southern separatists and the Hadi government over control of the southern half of the country.
"The Hadi government was nervous about any demonstration by the people, so they tried to stop it by force thinking that if there were a battle, the coalition would intervene and save them", the source said.
UAE is fighting against the internationally recognised Govt of Hadi who is living in exile in Saudi Arabia.
"The Arab coalition supporting legitimacy in Yemen ... calls on all Yemeni political and social components to be calm and to restrain themselves, adhering to the language of calm dialogue", it said in a statement, adding that it was important not to allow those who plotted to divide Yemenis to succeed.
"Those in southern part of city, including (ICRC staff) still unable to get out". There has been fierce fighting between the separatists and forces loyal to President Abdrabbuh Mansour Hadi who is now based in Aden.
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The separatists accused the prime minister of ordering his troops to open fire at the protesters.
Sunday's rally was called by the Southern Transitional Council, an autonomous body aimed at overseeing self-governance among southern provinces.
Former Aden governor Aidarous al-Zoubeidi formed the council in May a year ago after the President Abedrabbo Mansour Hadi fired him.
South Yemen was independent - with former British colony Aden as its capital - from its formation in 1967 until 1990, when it was unified with North Yemen under northern leader Ali Abdullah Saleh.
Dozens of people are reported injured, and at least 10 people have died.
On the other hand, Saudi-led coalition called on Sunday upon political parties for calm and restraint in connection to the recent developments in Aden, Saudi Press Agency reported. The two groups had been united throughout Yemen's three-year civil war against the Iranian backed Houthis in the north, However, the conflicts could hinder the efforts of the coalition to control the Iranian expansion plans in Yemen.