A long-running court battle over Britney Spears’ conservatorship has taken another turn, with the star’s father accused of “extorting” her.

The singer’s lawyer has filed documents demanding her dad step down immediately and without conditions from his role as conservator of her estate.

Mathew Rosengart has accused Jamie Spears of trying to link his departure from his 13-year-long role with payment of some $US2 million ($2.7 million) in fees to his lawyers and for experts handling the media.

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“Britney Spears will not be extorted,” Mr Rosengart said in documents filed with Los Angeles Superior Court on Monday (local time).

“Mr Spears’ blatant attempt to barter [his] suspension and removal in exchange for approximately $2 million in payments, on top of the millions already reaped from Ms Spears’ estate by Mr Spears and his associates, is a non-starter.”

Jamie Spears said for the first time earlier this month that he would relinquish control of his daughter’s $US60 million estate because he did not believe that a public battle would be in her best interests.

But he gave no date for his departure and said he first wanted to get the latest bills for work by his attorneys approved by the court.

Under conservatorship rules, Britney Spears pays for all costs incurred by her and others.

“Having finally acknowledged that his time as conservator should end, Mr Spears is obligated to step down without condition and without seeking to extract anything further from his daughter,” Mr Rosengart said in the filing.

The next court hearing in the increasingly contentious case is set for September 29.

Mr Rosengart said if Jamie Spears refused to immediately resign, the court “must” decide to suspend him from that date.

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Jamie Spears has controlled much of his daughter’s life since 2008 when she suffered a mental health breakdown.

The pop sensation, now 39, has been trying for more than a year to remove her father from the conservatorship and has refused to perform again while he remains in place.

In July, Britney Spears spoke in court for the first time about how his position of power had been detrimental to her.

She listed a series of grievances, alleging her father had been cruel and abusive. She claimed her hair vitamins had been taken from her and she was forced to take birth control.

“Mam, that’s not abuse, that’s just f—ing cruelty,” a tearful Spears told Judge Brenda Penny over the phone.

“Excuse my language but it’s the truth.”

The Toxic pop star has two sons, Sean and Jayden, who are both teenagers.

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She has been dating personal trainer Sam Asghari since 2016, and previously claimed that while they would like to get married and have children of their own – the conservatorship prevents it.

Jamie Spears has repeatedly said he has acted only in his daughter’s interests, to rebuild her finances and protect her from people trying to exploit her.

But her lawyer has stated that while Mr Spears maintains he should be allowed to step down on his own time, the singer’s testimony proves it to be an urgent matter.

“The world heard Ms Spears’ courageous and compelling testimony,” Mr Rosengart said.

“Britney Spears’s life matters. Her well-being matters. Every day matters. There is no time to waste.”

-with AAP