(Reuters) -Wall Street's top regulator told the White House in March it had already made substantial progress toward meeting President Trump and Elon Musk's demands for leaner government via voluntary workforce reductions, according to a planning document obtained by Reuters.

The U.S. Securities and Exchange Commission also told the Office of Management and Budget that it is legally required to seek input from Congress before any "significant reorganization" and that changes beyond certain budget thresholds need lawmakers' approval, according to the March 13 document provided in response to a Reuters' public records request.

The SEC submission for "reduction in force" and reorganizations, which Reuters is the first to report, responded to February's call from Trump and erstwhile ally Musk for federal agencies to develop plans for "large scale" cuts as part of the so-called Department of Government Efficiency initiative.

Though much of the text, released under the Freedom of Information Act, is redacted, the visible portions suggest agency leadership at least in part believed voluntary reductions already in progress could weigh against the need for further cuts.

An SEC spokesperson declined to comment beyond recently installed SEC Chair Paul Atkins's public statements and the agency's recent budget request. The Office of Management and Budget did not respond to a request for comment.

Since he took office in January, Trump's government-slashing efforts have stirred unease and concern among some SEC staff uncertain about the future of the agency's workforce and its political independence.

Critics have said the workforce reductions could hinder the SEC's performance in times of crisis but Atkins has brushed off such concerns.

Officials affiliated with the so-called Department of Government Efficiency continue to work on restructuring and cost cutting at the SEC.

The March plan was compiled by then-Acting Director Mark Uyeda, who while serving as interim agency chief also rewired top agency positions in Enforcement and Examinations to have them report to new deputy directors. Uyeda declined to comment on the document.

The plan predates Atkins' arrival in office in April.

In response to an OMB query about how the agency planned to achieve staffing cuts and costs savings in the next three fiscal years, the document highlighted workforce reductions already underway.

The "SEC has already used a variety of tools to achieve efficiencies," the memo said, referring to early retirement and resignation programs.

It also said that, in addition to voluntary departures, the SEC had "eliminated over 550 authorized positions," leaving agency headcount at that point at 4,300 and falling.

"This is below the lowest headcount level during the president's first term in office," it added.

Agency data previously released to Reuters shows that by April 600 people had taken the administration's various buyout offers. The SEC last month asked Congress to approve funding for the coming fiscal year that would roughly preserve staffing at around 4,100 full-time positions.

In response to a query about working with Congress on agency restructuring, the Uyeda plan pointed out that legally any "significant" restructuring required consultation with the House and Senate appropriations committees and that major funding shifts required those committees' approval.

(Reporting by Douglas Gillison in Wasington and Chris Prentice in New York;)