When China’s leaders wanted to send a message to the Biden administration last summer, they did what came naturally. They called Henry A. Kissinger.

Mr. Kissinger was 100 years old by then and had left the government 46 years earlier. But for as long as anyone could remember, the Chinese had venerated him as the secretary of state who forged the landmark diplomatic opening to Beijing. They had used him as a channel to Washington ever since.

Knowing him as they did, the Chinese played to his sense of self regard during his visit in July. They feted and flattered him. They put him up in the same guest quarters he had occupied during his historic visits in the 1970s. They hosted meetings in the same building where he had met their predecessors. And President Xi Jinping told Mr. Kissinger that his initial visits had led to 50 years of mostly stable relations and that he hoped this trip would usher in another 50 years.

That last part was the point. After months of friction over a spy balloon and other provocative actions, Mr. Xi was trying to make clear to President Biden’s administration that he wanted to put the tension behind them and repair ties with the United States. Mr. Kissinger returned home and dutifully filled in Secretary of State Antony J. Blinken by phone; met with William J. Burns, the C.I.A. director; and passed along his impressions to Jake Sullivan, the national security adviser.

The only thing unusual about the episode was how not unusual it was, at least for Mr. Kissinger. Until just weeks before he died on Wednesday, the centenarian diplomat was still a player on the world stage, still an occasional intermediary between governments, still a voice respected by the establishment of both parties, although not by his most virulent critics on the left and right.

He traveled the globe at an age when most of his contemporaries had either died or retreated to a retirement home. There were few if any doors in capitals around the world that did not open to him, although he always insisted he only met with heads of state at their invitation, not his own initiative. He was, at that late hour, still the toast of Davos.

“Kissinger’s life mission was to help create and maintain order in an international system that was always threatening to spin out of control,” said Martin S. Indyk, a former Middle East peace envoy for President Barack Obama and author of “Master of the Game,” about Mr. Kissinger’s diplomacy in the region. “This fueled an insatiable urge to influence the relationships between world leaders even up to his last days on earth.”

Gen. Jack Keane, a retired Army vice chief of staff, got to know Mr. Kissinger during years on the Defense Policy Board, which advises the Pentagon. He saw the former secretary in New York just a few weeks ago to talk about Russia, China, the Middle East and other searing issues of the day.

“It’s nothing short of remarkable,” he said. “I don’t think there’s a single person who has that kind of influence that he had, including our former presidents.”

Mr. Kissinger’s enduring presence in the halls of power, even with a visitor’s pass, stood out. It is probably not a stretch to assume that no other senior American figure in history ever kept himself in the mix quite as much at age 100. Mr. Blinken said on Wednesday that he last received advice from Mr. Kissinger as recently as a month ago.

“Few people were better students of history — even fewer people did more to shape history — than Henry Kissinger,” Mr. Blinken said while in Israel emulating Kissingerian shuttle diplomacy.

But that did not mean Mr. Kissinger was as influential as he once had been. His brand of realpolitik diplomacy, sometimes detached from questions of moral obligation or ideological commitment, had fallen out of favor with many. While he was readily given visitor’s passes to the halls of power, he was still reviled by many liberals as a war criminal and by many conservatives as an appeaser. “Henry Kissinger: Good or Evil?” read one headline in 2015.

He provoked a storm of indignation in some quarters just last year, when he suggested that the way to end the war in Europe was for Ukraine to cede some of its territory to Russia. By early this year, though, he had pivoted, saying that while he had previously opposed NATO membership for Ukraine, he now believed it should be admitted.

But even if critics were laying into him, at least they were listening. Mr. Kissinger always wanted to be paid attention to.

“I disagree with him on any number of things on China right now, but he was a man with genuine intellectual curiosity, which was a source of energy and a driving force,” said Representative Mike Gallagher, Republican of Wisconsin, who met Mr. Kissinger a couple months ago and found himself impressed.

Mr. Gallagher, who describes himself as more hawkish on China than the former secretary, nonetheless said it was a mark of Mr. Kissinger’s sustained stature that the Chinese Communist Party still saw him as a vital interlocutor, as demonstrated by last summer’s visit. “It’s crazy to think that even at that age, the C.C.P. was going to him first to give the sense of direction they wanted to take the relationship,” he said.

Mr. Kissinger’s interventions were not always welcomed by his successors or the presidents they served. There was, at times, a not-this-again sensation at the White House when his latest trip was announced or his latest memo arrived. Mr. Kissinger’s answer to many diplomatic challenges was to send Mr. Kissinger. More than one national security adviser was tasked with figuring out how to keep him on the leash.

And he could be characteristically Machiavellian even into his 90s. When Donald J. Trump came to power, Mr. Kissinger advised nervous German officials seeking reassurance about the new president to meet with Jared Kushner, his son-in-law and senior adviser. But unknown to the Germans, Mr. Kissinger had told Mr. Kushner that the allies were nervous about Mr. Trump and that he should use that to his own advantage. Don’t reassure them, he advised — keep them on edge.

Nor did it go unnoticed that his continuing prominence and access was helpful to his geopolitical consulting business.

Still, he was indefatigable. General Keane said Mr. Kissinger told him that after flying halfway around the world, his meeting with Mr. Xi lasted three hours and he had similarly long meetings with other officials.

“He’s 100 years old — I mean, God almighty,” General Keane said. “It never stopped him from going to dinners, to luncheons, international travel. He kept an extraordinary international schedule, really quite remarkable.”

Mr. Kissinger kept himself in the conversation by churning out books — 21 in all — and articles. As he completed his 10th decade, he made himself improbably into a guru on, of all things, artificial intelligence. His last op-ed piece was published just last month with Graham Allison in Foreign Affairs magazine arguing for cooperation between the United States and China to avoid an arms race on artificial intelligence, and warning of “catastrophic consequences” if they fail to do so.

The last public speech recorded on his website was delivered just six weeks ago, on Oct. 19, to the Alfred E. Smith Memorial Foundation Dinner, nearly half a century after he addressed the same event in 1974. “We need a combination of the visionary and the tactical,” he said on that night last month. “Few of our foreign policy challenges will lend themselves to purely visionary solutions. Paradoxically, if we are to avoid permanent conflict, most of them require a gradual approach and sustained effort.”

A week later, citing a broken bone sustained in a fall, he canceled a scheduled trip to Houston, where he was to join two successors, James A. Baker III and Hillary Rodham Clinton, for a panel discussion at a gala dinner marking the anniversary of the Baker Institute. He sent a video, in what was one of his last public messages.

“This celebratory evening takes place in a period of profound international disorder,” Mr. Kissinger said. “War has threatened Europe in the greatest way since World War II, and the Middle East tensions are building between the United States and China, two countries with the capacity to destroy the world. And artificial intelligence forebodes vast, potentially destabilizing technological changes across the world.

“These challenges notwithstanding, America requires capable capacities of changing the course for a more peaceful and prosperous world. To do so, however, we must develop a concept of where we are going and how we intend to get there across party lines and through political differences. Such is the requirement of leadership.”

The screen then went dark and Mr. Baker and Mrs. Clinton went ahead with the program without him. But in a surprise, the organizers then brought Mr. Kissinger back on the video screen at the end of the discussion to ask the final question.

“Who is the greatest secretary of state since World War II?” he asked puckishly.

Mr. Baker and Mrs. Clinton laughed. “I don’t know about you, Hillary, but my vote would be for Henry Kissinger,” Mr. Baker said.

Mrs. Clinton, knowing what fellow Democrats would say if she agreed, was more cautious, saying it was “an impossible question” and she did not “want to pick one person.” But she said, “I certainly think that he did a lot of incredibly important things.”