NEW YORK (Reuters) -Sharp downward revisions to past jobs data on Friday, followed by Trump's sudden order to fire the head of the Bureau of Labor Statistics, stoked investor fears about the integrity of economic data and the Fed's ability to read the true state of the economy.

News of a surprise weakening in the U.S. labor market last month jolted investors, while revisions to job figures for the past two months raised worries the U.S. central bank may have been flying blind in recent months and may need to play catch-up with interest rate cuts, investors said.

Fed Governor Adriana Kugler's early resignation from her term on Friday also potentially shakes up what was already a fractious succession process for Fed leadership amid difficult relations with Trump.

"Kugler's resignation allows the president to further shape the FOMC (Federal Open Market Committee) in his own image," said Jamie Cox, managing partner at Harris Financial Group.

Nonfarm payrolls increased by 73,000 jobs in July after rising by a downwardly revised 14,000 in June, the Labor Department's Bureau of Labor Statistics said in its employment report on Friday. Economists polled by Reuters had forecast payrolls increasing by 110,000 jobs after rising by a previously reported 147,000 in June.

The report comes two days after the U.S. central bank left unchanged its benchmark interest rate and avoided signaling imminent rate cuts, dialing back market expectations for an easing at the next policy meeting in September.

That changed dramatically on Friday, with odds for a 25 basis point cut in September jumping to around 81% after the data from 38% on Thursday, according to CME Group data.

"The Fed's job is becoming increasingly difficult based on the deterioration of the economic data," said Matthew Miskin, co-chief investment strategist at Manulife John Hancock Investments. "These revisions are massive and really are a game changer to the Fed's reaction function, and so I think this Fed meeting is one that they'd like to revise."

U.S. President Donald Trump on Friday said, without evidence, that numbers contained in the July jobs report from the Bureau of Labor Statistics were rigged. "In my opinion, today's Jobs Numbers were RIGGED in order to make the Republicans, and ME, look bad," Trump said in a Truth Social post.

He ordered that the commissioner of the Labor Department's Bureau of Labor Statistics Erika McEntarfer be fired after the data release.

"It's definitely a case of shooting the messenger," said Dean Smith, chief strategist at FolioBeyond. "Firing the head of BLS is not going to improve data collection and dissemination ... it's going to undermine confidence in the data going forward," he added.

'UNRELIABLE DATA?'

Revisions for May and June came in well above the norm, the Bureau of Labor Statistics said. It gave no reason for the revised data but noted that "monthly revisions result from additional reports received from businesses and government agencies since the last published estimates and from the recalculation of seasonal factors."

May's nonfarm payroll gain was slashed by 125,000, from 144,000 to just 19,000, while June's downward revision was by 133,000. In total, employment over the two months is now 258,000 lower than initially reported.

"It is painfully obvious that the U.S. government has an improper model for payroll calculations," said Michael Green, portfolio manager at Simplify Asset Management. "If you don't have reliable data, you make bad policy."

Spencer Hakimian, founder of macro hedge fund Tolou Capital Management, said layoffs across several government departments, part of Trump's plans to reduce wasteful government spending, have prompted him to rely more heavily on alternative measures of economic strength than just government data, such as credit card data, and data from Truflation, an independent inflation index alternative to official government inflation measures.

Fed Chair Jerome Powell said in a press conference on Wednesday the labor market remained strong, and that the central bank was still in the early stages of grasping how Trump's overhaul of import taxes and other policy shifts would play out for inflation, employment, and economic growth.

"Had those figures been the initial prints a month or two ago it would have significantly changed the labor market narrative over the entire summer," said Adam Hetts, global head of multi-asset and portfolio manager at Janus Henderson Investors, in a note.

Treasury yields, which move inversely to bond prices, dropped on Friday, with benchmark 10-year yields down by a whopping 15 basis points to 4.22% - their biggest daily drop since April. Two-year yields were down by about 25 basis points to 3.69%, registering their biggest daily decline since August last year.

Stocks declined too, also weighed on by Trump's latest tariffs salvo. The benchmark S&P 500 index lost 1.6%, bringing stocks to their lowest since early July.

The deterioration in the labor picture comes amid steep U.S. tariffs on large trade partners that - while not as high as feared earlier this year - are still largely expected to worsen inflation and slow economic activity.

"With job creation at stall-speed levels and the tariff headwind lying ahead, there's a strong possibility of a negative payroll print in the coming months which may conjure up fears of a recession," said Jeff Schulze, head of economic and market strategy at ClearBridge Investments.