July 8 (Reuters) - A critical readout on Wednesday of the first Federal Reserve policy meeting overseen by Chairman Kevin Warsh may offer greater insight into the "family fight" the new central bank leader said unfolded over two days last month as officials opted to leave interest rates unchanged and emphasized their commitment to controlling inflation.

Among the biggest uncertainties surrounding the release of the minutes of the June 16-17 Federal Open Market Committee meeting is whether Warsh overhauls them in the same fashion he did the committee's post-meeting policy statement, which was stripped of all forward guidance and curtailed its descriptions of current economic conditions.

Fed policymakers at the meeting agreed unanimously to leave their benchmark rate unchanged in a range of 3.50% to 3.75%. Meanwhile, updated forecasts submitted by everyone but Warsh showed a committee that had shifted away from the rate cuts they previously had projected and was now divided between those who feel leaving rates unchanged is the best course this year versus those who see a need to raise them at least once in the face of inflation driven higher by the U.S.-Israeli war with Iran.

Inflation is running at roughly twice the Fed's 2% target, while the job market appears to have stabilized following a weakening trend through most of last year.

Warsh was appointed by President Donald Trump, who wants lower rates and berated previous Chair Jerome Powell for not delivering them fast enough. But Warsh struck a hawkish tone during his first press conference - repeatedly emphasizing the Fed's inflation-control mandate while scarcely referencing its maximum-employment goals. Investors now broadly expect at least one rate hike this year. 

The new chairman has promised major reforms for the central bank, and after the meeting he announced the formation of five task forces to review how the Fed conducts its business, covering everything from its communications strategy to what data it uses to assess the economy.

With the changes to the policy statement, the minutes could take on even greater weight in helping investors and analysts understand the Fed's thinking - unless the FOMC under Warsh pares back how much detail about the arguments and economic data presented at the meeting is provided.

In describing the different views expressed at the meeting and the rough number of Fed officials agreeing or disagreeing, the minutes can make different interest rate decisions seem more or less likely in the future, or even begin laying the groundwork for eventual shifts in monetary policy.

That can come close to the sort of forward guidance Warsh wants to avoid, a fact that has some analysts expecting the minutes to be shorter and likely more austere in terms of the information provided.

"Warsh explicitly avoided policy guidance in the statement and press conference, so it seems unlikely that he would permit such guidance via the minutes," said Steve Englander, head of North American macro strategy at Standard Chartered. "His image of a 'family fight' to characterize vigorous policy discussion may also carry the connotation of secrecy that is often associated with family fights."