Some expect that the potential alignment of views may usher in greater consistency from the Trump administration, but not necessarily on the positions America’s allies want.
With Mr. Trump’s new tariffs and the growing likelihood that he will abrogate the Iran deal, not to speak of his continued criticism of both NATO and the European Union, they are worried that Mr. Trump will further damage diplomatic relations.
“It’s tough these days to be an ally,” sighed one senior European ambassador to Washington, who would not be named in keeping with diplomatic protocol.
Mr. Tillerson’s ugly firing by Twitter underscored to allies and enemies that President Trump is “the decider,” as George W. Bush used to say.
But it is also another indication of a long trend toward the centralization of foreign-policy decision-making in the White House and away from the State Department, said Jeremy Shapiro, a former senior State Department official now with the European Council on Foreign Relations.
“Consecutive administrations have not trusted the State Department and increasingly written them out, and that’s worse today,” Mr. Shapiro said. “They have been losing some good, talented and dedicated people, but the truth is that those people weren’t in a position to help the administration anyway in what it wants to do.”
Some countries, like China, Japan and France, have focused their efforts on the White House and Mr. Trump himself. While many ambassadorships have gone unfilled, Mr. Shapiro said, that role in his view is increasingly less important in a world of modern media and communications.
“The more important problem is the way this administration treats allies and the Europeans,” he said. “But that’s not a Tillerson problem. It’s a Trump problem.”
These trends, plus Mr. Trump’s trust in his instincts rather than in expertise, had left America’s career diplomats alienated and demoralized.
Then came Mr. Tillerson, who decided to try to remake the department by cutting its budget by 30 percent and failing — or failing to get the White House — to appoint senior officials and ambassadors in critical places like Germany, Turkey, Brussels, Egypt and Seoul.
In response, many up-and-coming midcareer diplomats were fired or quit, causing R. Nicholas Burns, a former senior State Department official now at Harvard, and another diplomat, Ryan C. Crocker, to warn of the “dismantling of the foreign service,” which is facing “its greatest crisis” at a time “when we need it most.”
Mr. Tillerson’s short tenure also explodes a persistent myth that private sector experience is valuable in making the government work smarter and more efficiently, said Leslie Vinjamuri, a professor at SOAS University of London and an associate in the America’s program at Chatham House.
“Tillerson alienated his staff without improving America’s image abroad and failed to bring the media with him,” she said.
Many cheered Mr. Tillerson’s dismissal, including Martin Indyk, a former American ambassador now at the Brookings Institution, who said in a Twitter message that it was overdue and that Mr. Pompeo should bring back the career staffers who had quit in “despair.”
Jeffrey Hawkins, a career State Department official and former ambassador to the Central African Republic until he resigned last September, spoke for many diplomats.
“I don’t think there will be a Secretary of State less missed than Rex Tillerson,” he said. “This is a man who was declaring war on the institution” for a White House “led by people who don’t believe in the mission of the agency,” Mr. Hawkins said.
“This man apparently felt he was dealing with a broken institution that needed massive surgery,” he added. “Not only did it not cure it, it left the patient flatlined.”
Yet allies fear that Mr. Tillerson’s ouster silences a pragmatic voice for traditional Republican foreign and trade policies, one that European diplomats felt was often on their side.
They are especially worried now that Mr. Trump will in May repudiate the Iran nuclear deal, which Mr. Pompeo opposed from the start. They are already talking more seriously about how to protect European companies and banks from renewed American sanctions on Iran.
Whatever Mr. Tillerson’s failings, said Charles Grant, director of the Center for European Reform, “he was a mainstream Republican, he was one of the grown-ups.”
“On trade he was sensible and on Iran his view is the European view,” Mr. Grant added, “and it is worrying that the President may have a Secretary of State who might make it easier for him to pursue his course on Iran.”
Ellie Geranmayeh, an Iran expert at the European Council on Foreign Relations, noted that French, German and British diplomats had been working with Brian Hook, Mr. Tillerson’s senior aide, to pacify Mr. Trump on the Iran deal by developing new ways to restrain Tehran’s missile development and regional support for the Syrian government and groups like Hezbollah and Hamas, while still preserving the agreement.
“Tillerson was the comfort voice for Europeans, who would help identify the room for compromise,” she said. “But with Pompeo, the Europeans and Iranians should expect much less room for flexibility.”
From the Balkans to east and Central Europe, the disconnect and diminished influence of American diplomats has played out in other ways, too.
Last week, it was reported that President Andrej Duda of Poland had declined to take a call from Mr. Tillerson — apparently on the grounds that the two were not on equal footing. Mr. Duda’s office did not deny it.
In Asia there was similar confusion, especially with the prospect of a summit meeting between Mr. Trump and the North Korean leader, Kim Jong-un.
South Korean officials have been working through the White House and Mr. Pompeo at the C.I.A. already, as the State Department seemed increasingly sidelined.
Mr. Tillerson, after all, was chastised by Mr. Trump for suggesting negotiations with North Korea, and then was left out of the decision when Mr. Trump suddenly changed his mind.
As a remedy, some, like Prime Minister Shinzo Abe of Japan, have shifted to relying on direct, close relations with the president, rather than cabinet secretaries.
But it is not clear how much even such relations matter when President Trump makes decisions on impulse rather than through close consultation with advisers.
Like others, Japan, too, was left unnerved by Mr. Trump’s impromptu decision to hold a summit with Mr. Kim. Its foreign minister, Taro Kono, was planning to visit Washington later this week to meet Mr. Tillerson, and instead is likely instead to try to meet Mr. Pompeo.
On social media, an opposition lawmaker, Akihisa Nagashima, a former vice defense minister, praised Mr. Tillerson as a “sensible person” and commented: “I cannot help worrying that the U.S.-North Korea summit meeting will fail and that a turn to a course of military conflicts will be real.”
For China, like Japan, there was comfort in the perception that good relations start with Mr. Trump himself. But Mr. Pompeo’s harder-line views on North Korea and China itself were a major source of concern.
At the C.I.A., Mr. Pompeo called China “the great threat for the U.S. in the long term” and has warned about China’s efforts to infiltrate the United States military, tech and educational institutions.
“Pompeo advocates a preventive war against North Korea to prevent it from attacking the United States,” said Song Guoyou, deputy director of the Center for American Studies at Fudan University in Shanghai. “If Trump’s meeting with Kim Jung-un fails, the Trump administration will have a strong voice that supports a war against North Korea.”
In some corners there was outright anxiety.
“I doubt Pompeo will be a moderate force on U.S.-China relations,” said Bonnie Glaser, a China expert at the Center for International and Strategic Studies. “He is no panda hugger.”