Heavy fighting intensified at night after the two sides used tank and artillery on the second day of an attempted "coup" in the southern port city, military sources said.
The Saudi-led military coalition which supports the government called Tuesday for an immediate ceasefire and an end to "all forms of armed conflict", in a statement cited by Saudi state news agency SPA.
It said it would take "all necessary measures to restore security and stability" after earlier calls for restraint went unheeded.
The flare-up has added yet another dimension to one of the world's most complicated conflicts, a civil war that has left thousands dead and millions on the brink of starvation.
The head of the International Committee for the Red Cross mission in Yemen, Carlos Batallas, said on Twitter on Monday that the clashes in Aden had killed 36 people and wounded 185.
The ICRC did not provide figures on civilian casualties.
Residents were hunkered down at home as five separatist fighters were killed by snipers and four soldiers died in clashes, military sources said, with tanks and heavy artillery entering the fray.
The clashes came after separatist forces seized government buildings in what Yemen's prime minister called an attempted coup.
At night, pro-separatist security forces advanced in some areas and were just one kilometre (mile) away from the presidential palace in Aden, security and military sources told AFP.
They also seized two military camps near Aden international airport which remained closed for the second day, the sources said.
Aden has served as the headquarters of Saudi-backed President Abedrabbo Mansour Hadi's government since it was forced out of the capital Sanaa by Huthi rebels three years ago.
The separatists -- who want the return of the independent South Yemen that existed before 1990 -- supported Hadi's forces against the Shiite rebels, but tensions between them have risen in recent months.
'Shooting' all night
Fighters from both sides have been deployed in most areas of Aden, paralysed for a second day after 15 people were killed and dozens wounded on Sunday.
Universities, schools and shops stayed closed, an AFP photographer said.
The hostilities erupted early Sunday when pro-government troops prevented supporters of the separatist Southern Transitional Council from entering Aden for a rally.
Separatists have dispatched additional forces from the central province of Marib and the southern province of Abyan, security sources said.
The forces from Abyan marched on Aden after clashes with loyalists on the way.
After the separatists seized the government headquarters on Sunday, Prime Minister Ahmed bin Dagher denounced a "coup... in Aden against legitimacy and the country's unity".
He urged the Saudi-led coalition to intervene in its defence.
The coalition launched air strikes against the Iran-backed Huthi rebels in March 2015 and sent troops to support Hadi's forces, fearing that Tehran would gain a foothold in the country on Saudi Arabia's southern border.
On Sunday, security sources said pro-separatist units trained and supported by the UAE had taken over the government headquarters after clashes.
The International Committee of the Red Cross said fighting continued overnight.
"All night shooting in Aden #Yemen, including heavy weapons," Alexandre Faite, the head of the ICRC delegation in the country based in Sanaa, said on Twitter.
"Those in southern part of city, including (ICRC staff) still unable to get out."
UN envoy to Yemen Ismail Ould Cheikh Ahmed urged all parties to return to "calm and dialogue".
The negotiator is to step down in April after three years overseeing UN-brokered negotiations between the government and rebels, none of which have stemmed the violence.
More than 9,200 people have been killed in Yemen since the Saudi-led coalition intervened.
The separatists joined forces with Hadi's government to oust the rebels from southern provinces in 2015, but tensions have soared since a secessionist governor's sacking last year.
Three civilians were among the 15 people killed on Sunday, hospital sources said, after separatist protesters were prevented from entering Aden for an anti-government rally.
The separatists accused the premier of ordering his troops to open fire on the protesters.
Sunday's rally was called by the Southern Transitional Council, an autonomous body not recognised by the government and aimed at overseeing self-governance in southern provinces.
Former Aden governor Aidarous al-Zoubeidi formed the council in May last year after Hadi fired him.
The council had asked Hadi to make changes in the government, accusing it of corruption and mismanagement, and gave him a week to do so -- a deadline that expired on Sunday.
It had warned that if Hadi did not accept the demand, its supporters would begin a protest campaign to oust Dagher's government.
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.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)