He said that locality pay increases would cost 25 billion dollars (£19 billion), on top of a 2.1% across-the-board increase for most civilian government employees.
Cox said federal worker pay and benefits have been cut by more than $200 billion since 2011, and workers are now earning 5 percent less than they did at the start of the decade.
Congress has an opportunity to effectively overrule the President's edict if lawmakers pass a spending bill that includes a federal pay raise.
Rep. Gerry Connolly, D-Va., who represents many federal workers, blamed what he said was Trump's mismanagement of federal government.
The president cited his authorities under Title 5, United States Code to implement pay adjustments in response to national emergencies and serious economic conditions.
Trump cited the "significant" cost of employing federal workers as justification for denying the pay increases, and called for federal worker pay to be based on performance and structured toward recruiting, retaining and rewarding "high-performing Federal employees and those with critical skill sets". "Across-the-board pay increases and locality pay increases, in particular, have long-term fixed costs, yet fail to address existing pay disparities or target mission critical recruitment and retention goals".
In a letter to House and Senate leaders, Trump described the pay increase as "inappropriate".
"These numbers are very, very sustainable - this isn't a one-time shot", he said last month after figures showed the U.S. economy grew at a 4.1% annual rate in the second quarter of the year. A judge struck down most of those provisions last week.
The pay raise matter was the latest in a string of moves that reflect an attempt to rein in spending on federal employees. Federal worker unions pledged to fight these reforms.
"Zero. This seems to be how much respect President Trump has for federal workers", wrote Sen. The president last year signed a package of tax cuts that is forecast to add about $1.5 trillion to federal deficits over 10 years. "I can think of nothing more hypocritical or disingenuous than to turn around and throw hardworking federal employees under the bus on the pretext of fiscal responsibility". This proposal included substantial cuts to retirement funds. A veto of a spending bill could lead to a federal government shutdown.