By Gavin Jones

ROME (Reuters) - The travails of the anti-establishment 5-Star Movement's mayor of Rome mounted on Thursday when she announced the departure of the city's finance chief whom she appointed just four days ago.

Virginia Raggi has been beset by problems since winning a landslide victory in June to become Rome's first woman mayor, dealing a potential blow to 5-Star's credentials to win office at national elections due in 2018.

A mix of resignations, infighting and scandal reached almost farcical proportions on Thursday when Raggi announced that "by common accord" she was parting company with the head of Rome's finance department Raffaele De Dominicis.

She hired De Dominicis - a retired magistrate - on Sunday to replace Marcello Minenna, who stepped down three days earlier along with Raggi's chief of staff and the heads of the city's trash collection and public transport companies.

Those resignations were a chain reaction to the forced departure of the chief of staff, who it emerged had not been hired according to legally correct procedures.

Raggi wrote on her Facebook page that she had "just learned" that De Dominicis did not have the necessary requirements to fill the post on the basis of 5-Star's internal party rules. She did not give further details.

"I am bitter, I consider myself the victim of an unprecedented plot," De Dominicis told news agency AGI.

5-Star has built its fortune on denouncing the graft that plagues Italy's traditional parties, and according to opinion polls it is neck-and-neck with Prime Minister Matteo Renzi's Democratic Party as the most popular political force.

However, the turmoil in Rome has dented the party's image, with its national leadership being sucked into Raggi's problems.

On Wednesday Luigi Di Maio, the lower-house deputy widely tipped to be its candidate for prime minister, apologized to voters after it was revealed he had known for weeks that one of Raggi's team was under investigation for alleged wrongdoing, but had not made it public.

The resignations mean Raggi now finds herself without a finance chief, a chief of staff, a deputy chief of staff or a head of the city's trash collection company.

The party's top brass, including its founder, comedian Beppe Grillo, tried to hit back at a rally on Wednesday where they accused 5-Star's opponents of conspiring to destroy it and promised to bounce back stronger than ever.

However, De Dominicis's departure suggests Raggi's difficulties are far from over and the movement seems dangerously divided at the city level.

On Thursday three members of a so-called "directorate" of senior 5-Star politicians set up to support and advise Raggi in running Rome announced that they were also resigning, saying the mayor should move ahead under her own steam.

(Editing by Crispian Balmer and Richard Balmforth)