Mr. Trump’s first appointee to head the E.P.A., Scott Pruitt, and his first appointee to head the Interior Department, Ryan Zinke, resigned last year after thousands of pages of documents released under Freedom of Information Act requests raised questions about matters such Mr. Pruitt’s alleged spending abuses, first-class travel and relationships with lobbyists, and Mr. Zinke’s efforts to secure taxpayer-funded perks for his wife.

Both men have said that the criticism of their actions was politically and personally motivated, and that they did nothing wrong.

Last year, the Interior Department implemented a new “awareness policy” regarding requests for information and public records under the Freedom of Information Act. The new policy requires career staff reviewing such requests to notify politically appointed officials if their names or email addresses appear in documents that have been designated to be released.

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That policy, watchdog groups say, has allowed top officials appointed by President Trump to then withhold or delay the release of such information. “The upshot is that, in practice, the policy has morphed from a procedure that provides awareness to political appointees to one that allows political appointees to unlawfully withhold and delay documents,” said Travis Annatoyn, senior counsel at Democracy Forward, a watchdog group that has requested an Interior Department investigation into the matter.

A spokeswoman for the Interior Department, Molly Block, declined to comment and referred to the Interior Department’s website, which includes a document describing the policy. The page says the policy is intended to streamline the process of the agency’s response to increased Freedom of Information Act requests.