* Rivals signed deal in 2015 but still wrangled over terms
* Former rebel Machar finally returned to capital in April
* This week's clashes are first in Juba since Machar's return
* Experts fear slide back into civil conflict (Recasts with U.N. Secretary-General Ban Ki-moon statement)
By Denis Dumo
JUBA, July 8 (Reuters) - United Nations chief Ban Ki-moon said on Friday he was deeply alarmed by fighting in South Sudan's capital Juba between rival troops, describing the violence threatening a fragile peace process as a "new betrayal" of the country's people.
President Salva Kiir and former rebel leader Riek Machar, now vice president, called for calm on Friday at the State House, where the rivals had been in talks when the fighting flared on Thursday between groups loyal to each of them. Five people were killed.
A Reuters witness heard further shooting in Juba on Friday. Both leaders said they did not know what prompted Friday's incident. South Sudanese radio urged citizens to stay at home.
It was the first eruption of violence in Juba since Machar returned in April, under a deal to end two years' of civil war. Ban described the fighting as "yet another illustration of the parties' lack of serious commitment to the peace process."
Ban urged Kiir and Machar to put an immediate end to the fighting, discipline the military leaders responsible for the violence and finally work together to implement the peace deal.
"(The fighting) represents a new betrayal of the people of South Sudan, who have suffered from unfathomable atrocities since December 2013," the Secretary-General said in a statement.
"I am also gravely concerned by the resurgence of violence in Wau and Bentiu, which could lead to a dramatic deterioration of the security situation across the country," Ban said.
Experts have warned that the five-year-old nation risks sliding back into conflict unless the two sides move more swiftly to implement the peace pact, including ensuring the swift re-integration or demobilisation of rival combatants.
"All we want to tell the public now is that they should remain calm," Machar said at a joint news conference with Kiir on Friday. "This incident also will be controlled, and then measures will be taken so that peace it restored."
Kiir's SPLA and Machar's opposition SPLA-IO fought for more than two years during the civil war.
Late on Thursday, at least five soldiers were killed in a clash that started when a group of soldiers backing Kiir had stopped vehicles carrying Machar loyalists in Gudele, a district of Juba where Machar has his political base.
A spokesman for the opposition SPLA-IO, Colonel William Gatijiath Deng, said fighting began after Machar's forces refused to allow their vehicles to be searched. (Additional reporting by Reuters television and Michelle Nichols at the United Nations; Writing by Edmund Blair and Michelle Nichols; Editing by Andrew Heavens and Richard Chang)
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