Britney Spears’s father said in a new court filing he would step down at some point from the helm of the controversial conservatorship that has governed the pop star’s personal life and roughly $60 million estate for the last 13 years.

The court documents, filed in Los Angeles County Superior Court on Thursday, come weeks after the 39-year-old star asked a judge presiding over the case to remove her father, James P. Spears, calling the conservatorship “abusive.”

A new lawyer for Ms. Spears, Mathew Rosengart, has moved aggressively in recent weeks to remove or suspend Mr. Spears. It is part of a broader effort to terminate the conservatorship over Ms. Spears, an obscure legal arrangement that has been in place since 2008 when it was instituted for her protection due to mental-health issues and potential substance abuse. Ms. Spears acknowledged its necessity at the time.

Mr. Spears maintained that there are “no actual grounds for suspending or removing” him, but said that he “does not believe a public battle with his daughter over his continuing service as her conservator would be in her best interests."

“There are no urgent circumstances justifying Mr. Spears’s immediate suspension,” the filing states. “It is highly debatable whether a change in conservator at this time would be in Ms. Spears’s best interests.”

At the same time, Mr. Spears said he would work with the court and Ms. Spears’s lawyer "to prepare for an orderly transition to a new conservator,” according to the documents.

Mr. Rosengart, the lawyer for Ms. Spears, praised the move in a written statement. “It is vindication for Britney,” he wrote. "We are disappointed, however, by [the] ongoing shameful and reprehensible attacks on Ms. Spears and others.”

Mr. Rosengart wasn’t immediately available for further comment. A lawyer for Mr. Spears couldn’t be immediately reached.

Mr. Rosengart has said in previous filings that the proposal to remove Mr. Spears was supported by Lynne Spears, the pop star’s mother; Ms. Spears’s medical team; and Jodi Montgomery, who currently serves as conservator of Ms. Spears’s personal affairs. (Mr. Spears relinquished that role in 2019.)

Mr. Spears has long insisted that he has been trying to protect his daughter; he has also taken some credit for her professional rebound years ago. “Mr. Spears has always done what he believes was in his daughter’s best interests,” the filing says.

The next hearing in the case is scheduled for Sept. 29. Judge Brenda Penny, who is overseeing the case, recently denied a petition by Mr. Rosengart to bring the hearing forward.

Write to Neil Shah at neil.shah@wsj.com