The administration said it would also post union contracts online so that Americans could review its efforts to negotiate better deals with government workers.

The third order aims to cut down on “official time,” in which government workers who have roles in the union, like helping colleagues file grievances, are allowed to perform those roles during normal working hours for which they draw their usual salary. (An analogous concept exists for private-sector unions.) The order limits official time to 25 percent of their hours during the year.

Administration officials said a subset of federal employees had been able to spend as much as 100 percent of their duty hours on union business, and estimated savings of at least $100 million a year once the order is fully in effect.

Mr. Bremberg, the White House domestic policy official, said the actions would make good on the president’s call to “empower every cabinet secretary with the authority to reward good workers and remove those that undermine the public trust or fail the American people.”

The executive order making it easier to fire poor-performing workers was an effort to expand on legislation that Congress enacted last year aimed at the Department of Veterans Affairs, which became embroiled in a scandal in 2014 over the extremely long waits that veterans were enduring for health care.

According to data collected by the American Federation of Government Employees, more than 1,600 workers have been removed under the provisions of the law passed last year, called the Department of Veterans Affairs Accountability and Whistleblower Protection Act. Among those removed were over 200 housekeeping aides, nearly 150 nursing assistants and nearly 100 food-service workers — representing three of the top four positions with the most removals.

Donald F. Kettl, a professor of public policy at the University of Texas at Austin who is based in Washington, said the number of low-level employees removed suggested the department was not using the legislation to make structural reforms that would improve veterans’ access to care.