"Those in southern part of city, including (ICRC staff) still unable to get out".
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 after Hadi fired him the previous month.
Aden, Yemen's second largest city, used to be the capital of the once independent South Yemen before unification in 1990.
More than 9,200 people have been killed in Yemen since a Saudi-led military coalition intervened to support Hadi's government in its fight against the rebels in 2015.
According to the Sputnik source, heavy clashes are taking place in the area: the government forces are fighting with the separatists. 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. The government has now asked neighbouring countries to help, including the Saudi-led coalition.
The Houthis have increasingly consolidated their grip on Sanaa and the north, especially since rebels killed Saleh in December after their alliance collapsed.