AFGE is the largest federal employee union and represents most civilian workers at Robins Air Force Base.
In a letter to Congress on Tuesday, Obama said the current two-year freeze should be extended at least until March and Congress passes a budget.
J. David Cox Sr, AFGE's national president, said the president's decision was unwarranted and unjustified.
"He could have used his authority under the Federal Employees Pay Comparability Act to set the pay alternative pay plan at 0.5 percent," Cox said in a statement released Tuesday. "Instead, he contradicted his own fiscal year 2013 budget promise of an end to the pay freeze."
Cox said federal workers are the lone Americans who have made sacrifices to reduce the nation's deficit. He noted that federal civilian employees have lost some $60 billion in salaries over the past two years along with substantial cuts to retirement benefits.
"The contractor workforce, a group that is three times the size of the federal workforce and substantially more expensive in terms of salaries and benefits, has not been asked to sacrifice one red cent," the AFGE president stressed.