WASHINGTON — At the State Department, the normally pulsating hub of executive offices is hushed and virtually empty. At the Pentagon, military missions in some of the world’s most troubled places are being run by a defense secretary who has none of his top team in place. And at departments like Treasury, Commerce and Health and Human Services, many senior posts remain vacant even as the agencies have been handed enormous tasks like remaking the nation’s health insurance system.

From the moment he was sworn in, President Trump faced a personnel crisis, starting virtually from scratch in lining up senior leaders for his administration. Seven weeks into the job, he is still hobbled by the slow start, months behind where experts in both parties, even some inside his administration, say he should be.

The lag has left critical power centers in his government devoid of leadership as he struggles to advance policy priorities on issues like health care, taxes, trade and environmental regulation. Many federal agencies and offices are in states of suspended animation, their career civil servants answering to temporary bosses whose influence and staying power are unclear, and who are sometimes awaiting policy direction from appointees whose arrival may be weeks or months away.

“There’s no question this is the slowest transition in decades,” said R. Nicholas Burns, a former State Department official who served under presidents of both parties and has been involved in transitions since 1988. “It is a very, very big mistake. The world continues — it doesn’t respect transitions.”

Mr. Trump has insisted that the barren ranks of his government are not a shortcoming but the vanguard of a plan to cut the size of the federal bureaucracy. “A lot of those jobs, I don’t want to appoint, because they’re unnecessary to have,” Mr. Trump told Fox News last month. “I say, ‘What do all these people do?’ You don’t need all those jobs.”

But the president has not proposed any plan for trimming crucial senior positions, and a White House spokeswoman, Lindsay E. Walters, said he eventually planned to fill them.

Mr. Trump’s personnel problems are rooted in a dysfunctional transition effort that left him without a pool of nominees-in-waiting who had been screened for security and financial problems and were ready to be named on Day 1. In the weeks since, the problem has been compounded by roadblocks of his own making: a loyalty test that in some cases has eliminated qualified candidates, a five-year lobbying ban that has discouraged some of the most sought-after potential appointees, and a general sense of upheaval at the White House that has repelled many others.

Officials involved in and briefed on the situation described it on the condition of anonymity, unwilling to be quoted disparaging Mr. Trump or his administration.

But the numbers paint an unmistakable picture. While Mr. Trump has won confirmation of 18 members of his cabinet, he has not nominated anyone for more than 500 other vital posts and has fallen behind his predecessors in filling the important second- and third-tier positions that carry out most of the government’s crucial daily functions. As of Sunday, he had sent to the Senate 36 nominations for critical positions, just over half of the 70 sent by President Barack Obama, who was also criticized for early delays, at the same point in 2009, according to figures compiled by the nonpartisan Center for Presidential Transition at the Partnership for Public Service.

In the vast majority of cases, Mr. Trump’s administration has not even begun the lengthy screening process — which can take several weeks to as long as two months — that nominees must complete before their confirmations can be considered by the Senate. According to data obtained by The New York Times, the Office of Government Ethics, the independent agency that conducts financial reviews of every presidential nominee, had received only 63 disclosure reports for prospective Trump administration nominees as of March 5, less than a third of the 228 that Mr. Obama’s team had submitted by that date in 2009.

At the State Department, both deputy-level jobs remain unfilled, along with the posts of six under secretaries and 22 assistant secretaries. At the Treasury Department, Mr. Trump has yet…