* Aden violence opens new front in Yemen conflict
* Saudi Arabia says there is no alternative to the govt
* Fighting may further fragment the country
* Jeddah hosts talks between Aden combatants (Adds Saudi statement on clashes in south Yemen)
By Marwa Rashad and Mohammed Mukhashaf
RIYADH/ADEN, Sept 5 (Reuters) - Saudi Arabia called on southern Yemeni separatists on Thursday to cede control of Aden and voiced its support for the government, an indication that its rift with close ally United Arab Emirates had deepened.
In a statement carried by the state news agency SPA, the kingdom refused any "new reality" imposed by force in the south and added any attempt to destabilise Yemen's security would be a threat against the Kingdom and "will be dealt with decisively".
Saudi Arabia, leader of an Arab coalition battling Yemen's Iran-aligned Houthis, is hosting indirect talks to resolve the crisis between the UAE-backed separatists and officials of the government of President Abd-Rabbu Mansour Hadi, which has opened a new front in Yemen's war.
The breakaway movement is part of the coalition that intervened in Yemen in March 2015 to try to restore Hadi's government which was ousted from power by the Houthis in the capital Sanaa in late 2014.
But the separatists seek independence and turned on the government in early August and captured Aden, its interim base. Southern fighters have clashed with government forces elsewhere in the south as they tried to extend their reach.
On Thursday, they organised a rally in Aden where thousands of Yemenis gathered in support of the UAE, which backs separatists who seized the southern city from the Saudi-backed government in a power struggle that has strained Riyadh's alliance with its main regional partner the UAE.
March organisers said they wanted to show loyalty to the UAE, the second power in the coalition, which openly intervened to support the separatists by launching air strikes on government forces last week when they tried to recapture Aden, forcing them to withdraw.
Men, women and children gathered in Aden's main al-Maalla street, waved Emirati flags and colours of the former South Yemen republic, which the separatist Southern Transitional Council (STC) aspires to revive.
"This is the least we can do for the UAE which has given everything to the people of South Yemen," said Hashem al-Morshidi, one of the demonstrators.
Others carried banners expressing loyalty to the UAE or portraits of Abu Dhabi's leaders as large speakers blared Emirati music.
Hadi's government has publicly asked the UAE to stop supporting separatist forces. Abu Dhabi has responded by criticising his government as weak and ineffective.
The fight for Yemen's south threatens to further fragment the Arabian Peninsula nation and hamper United Nations efforts to end the conflict that has killed tens of thousands and pushed millions toward famine.
Saudi Arabia called on both sides to refocus on battling the Houthis, who hold Sanaa and most major urban centres. It has held indirect talks between STC leaders and Yemeni government officials for that purpose in the Red Sea port city of Jeddah this week.
"There is no alternative to the legitimate government in Yemen and any attempts to impose a new reality by force will not be accepted," the Saudi statement said. "The Kingdom stresses the necessity of handing over military bases as well as government and civilian buildings to the legitimate government."
U.N. special envoy Martin Griffiths tweeted on Thursday his support to the Jeddah talks.
Hadi's government has said it would not participate in a summit unless the STC hands back Aden.
"We will not sit with the so-called STC at the table," Interior Minister Ahmed al-Mayssari said in an audio recording shared by government officials on Wednesday.
"If there must be dialogue it should be with the UAE ... it is the main party behind this conflict between us and the STC is only a political tool in their hands."
The UAE in June scaled down its military presence in Yemen but maintains influence via tens of thousands of southern separatist fighters it has armed and trained.
Abu Dhabi, which has called for a political solution to the standoff, said on Wednesday it was confident the Jeddah meeting would succeed. Yemeni sources have said that a summit could reshuffle Hadi's government to include the STC.
(Writing by Aziz El Yaakoubi; Editing by Ghaida Ghantous, William Maclean and Lisa Shumaker)