Mr. Putin said he was reducing the American government’s overall presence to the equivalent of the Russian presence in the United States. But the total staff includes more than just State Department diplomats; other American government agencies have employees stationed in Russia, including the Departments of Agriculture and Commerce, NASA and the Library of Congress.

American officials said the reduction ordered by Mr. Putin will have a significant effect on services, resulting, for example, in much slower processing of visas for Russian travelers to the United States. Another major function of any embassy is to collect local information and intelligence to inform policy makers back home, which will likely be hindered as a result.

“Cutting our staff by 755 people will do tremendous damage to our diplomatic mission in Russia,” said Michael A. McFaul, who was ambassador to Russia under President Barack Obama. “That our president does not appreciate this obvious fact suggests he doesn’t understand what embassies do in the pursuit of American national interests.”

Mr. Putin’s order was a delayed reaction to Mr. Obama’s seizing of two Russian diplomatic properties in the United States last year. The Obama administration also expelled 35 Russian diplomats after American intelligence agencies concluded that Moscow attempted to influence the 2016 presidential election.

But the embassy staff reduction was triggered by legislation — approved last month by near-unanimous bipartisan votes in both houses of Congress — mandating sanctions against Russia and curtailing Mr. Trump’s ability to lift them without a review by lawmakers. Mr. Putin, who like Mr. Trump has generally avoided direct criticism of his American counterpart, acted before the president signed the bill so that it would be a response to Congress rather than Mr. Trump.

With any veto certain to be overridden, Mr. Trump reluctantly signed the sanctions legislation. But he attached a signing statement to it, making clear that he considered some of the law’s provisions unconstitutional and leaving open the possibility that he might not abide by them as Congress intended.

Because the staff reductions are not required to take place until Sept. 1, some analysts noted the possibility that Mr. Putin was leaving room for a compromise to avert them from happening. But Mr. Trump expressed no concern about the embassy cuts, suggesting there would be no effort to try to reverse or mitigate the Russian decision.

Representative Kathleen Rice, Democrat of New York, chastised Mr. Trump for his comments. “This is insulting to US diplomats,” she wrote on Twitter. “Also, really, really stupid. Diplomats don’t get fired for getting kicked out of a hostile foreign country.”