* Renewed clashes in Tripoli, two reported killed in capital
* Renegade army general gaining support for anti-Islamist campaign
* Gunmen kill Chinese engineer in eastern city Benghazi
* New PM wants negotiations, inclusive cabinet (Recasts with renegade general)
By Ayman al-Warfalli and Ahmed Elumami
ABYAR/TRIPOLI, Libya, May 21 (Reuters) - A Libyan renegade general called on the government to hand over power to the country's top judges, mounting a challenge against Tripoli as heavy fighting erupted in the capital on Wednesday.
Western powers fear a call by General Khalifa Haftar for army units to join his campaign will split the nascent military and trigger more turmoil in the oil producing country which is struggling to restore order three years after the fall of strongman Muammar Gaddafi.
The government is unable to control the militias who helped oust Muammar Gaddafi in a NATO-backed 2011 uprising but are now defing authority.
"I call on the top judicial council to form a crisis government to oversee the next elections," said the retired general, dressed in uniform and surrounded by senior officers.
The council is independent and is one of the few state bodies respected by normal Libyans tired of anarchy and militias.
Haftar said government and parliament had lost any legitimacy because they were unable to purge the OPEC producer of extremists roaming around unchallenged.
His campaign got a boost after Libya's top air defence commander declared suppport for his campaign which kicked off on Friday with a strike against Ansar Sharia and other militant groups in the eastern city of Benghazi.
Culture Minister Habib Amin also announced his backing, the first government minister to join Haftar's forces. He said parliament had failed to fight "terrorists", echoing Haftar's rhetoric.
"I don't recognize the (General National) Congress (assembly) anymore," Amin told Reuters.
Tripoli residents reported several loud explosions early on Wednesday near the al-Yarmouk air defence barracks after air defence top commander Juma al-Abani released a video message saying he was joining "Operation Dignity", Haftar's campaign against Islamists.
Heavy fighting involving anti-aircraft machine guns mounted on trucks also broke out overnight near an army camp in Tajoura, an eastern suburb, witnesses said. The city was quiet by dawn.
At least two people from Mali died in the fighting, a health ministry source said.
Compounding the political chaos, state news agency LANA said on Wednesday the interior ministry had also joined Haftar's campaign, a report that was dismissed minutes later by the acting interior minister.
Libya has been plunged into turmoil since its 2011 uprising ended Muammar Gaddafi's one-man rule.
Many Libyans have grown frustrated with the government and parliament's failure to contain Islamist fighters and other militias who took part in rebellion and who have since openly defied the authorities to demand more oil wealth and power.
Haftar, a former Gaddafi ally who split with the autocrat in the 1980s, is the latest player to emerge in Libya's network of former fighters vying for control over parts of the country.
Culture Minister Habib Lamin, who has acted as cabinet spokesman, told Reuters some deputies had asked the government to arm the Islamist militant group Ansar Sharia to confront Haftar.
"The government rejected this," he said and, underlining tensions between government and parliament, accused deputies of having contributed to the chaos by approving militia funding in the past.
The parliament is split between Islamist parties loosely allied to the Muslim Brotherhood, the anti-Islamist National Forces Alliance, and scores of independents and tribal leaders of varying allegiances.
Western governments are concerned Libya's instability may worsen and spill over into its North African neighbours, who are still emerging from the political unrest following the 2011 "Arab Spring" revolts.
Libya's new Prime Minister Ahmed Maiteeq on Wednesday called for negotiations to end Libya's crisis and said he wanted to form a new cabinet open to all political factions which reject violence.
"I personally promise to hold negotiations with all sides," said Maiteeq, without mentioning Haftar by name, in his first press conference since he was elected this month in a chaotic parliamentary vote disputed by some lawmakers.
Militiamen, who Haftar later said were loyal to him, stormed the General National Congress (GNC), Libya's parliament, and fought for six hours with other armed groups on the airport road on Sunday.
Two days earlier, Haftar's troops had attacked Islamist militants in Benghazi in the worst clashes in the eastern city for months, killing more than 70 people.
In a further sign of unrest, gunmen abducted three Chinese engineers from their construction site in the eastern city of Benghazi on Tuesday, according to China's official press agency, Xinhua.
One was later found shot and died in hospital while his two colleagues were released, Xinhua reported. (Reporting by Ahmed Elumami, Feras Bosalum and Ulf Laessing; Writing by Ulf Laessing; Editing by Patrick Markey, Andrew Heavens)