Longtime employees at three of the agencies — including some career environmental regulators who conceded that they remained worried about what President Trump might do on policy matters — said such orders were not much different from those delivered by the Obama administration as it shifted policies from the departing White House of George W. Bush. They called reactions to the agency memos overblown. On Wednesday, Douglas Ericksen, a spokesman for the E.P.A., said that grants had been only briefly frozen for review, and that they would be restarted by Friday.

“I’ve lived through many transitions, and I don’t think this is a story,” said a senior E.P.A. career official who spoke on the condition of anonymity because he was not authorized to speak to the news media on the matter. “I don’t think it’s fair to call it a gag order. This is standard practice. And the move with regard to the grants, when a new administration comes in, you run things by them before you update the website.”

But the White House and State Department did delete nearly all mentions of climate change policy — which had been a top priority for Mr. Obama — and have begun replacing them with pages detailing Mr. Trump’s plans to roll back those policies — a top priority for the new president.

It is standard practice for new administrations to make changes to their websites to reflect their different policy positions. The full contents of the Obama administration’s White House and State Department websites, including working links to climate change reports, have been archived and are readily available to the public.

But environmental advocates and Democrats took advantage of the moves, noting that they appeared to target agencies that focus on environmental protection and scientific research, and calling them a chilling signal that the Trump administration intends to suppress communication about science and environmental policy, and possibly scientific data.