Mr. Quinn had become the subject of a battle between two camps in the White House: economic nationalists, who wanted him out, and more mainstream backers of free trade, who defended him.
Taken together, these developments constituted a potentially significant victory for the hard-liners, coming off a string of setbacks in their efforts to persuade the president to deliver on the most combative anti-free-trade planks of his presidential campaign.
But the ultimate outcome of this policy debate is still far from clear, several officials said. Mr. Trump does not plan to confront Mr. Xi with the most aggressive of his campaign threats: a 45 percent tariff on Chinese goods.
Nor is the United States likely to designate China a currency manipulator, something he promised to do as a candidate. Holding back those moves suggests Mr. Trump is also heeding the more moderate voices among his advisers, who argue that the United States cannot afford to ignite a trade war with China.
“The nativist and nationalist forces certainly have influence,” said Nicholas Lardy, an expert on the Chinese economy at the Peterson International Institute for Economics. “But it looks like it’s dwindling rapidly.”
Mr. Lardy said anti-dumping cases on steel were mostly symbolic, since American imports of steel from China accounted for only a few percentage points of the trade deficit. The Obama administration filed multiple anti-dumping cases with the World Trade Organization.
Still, the pitched battle over trade policy, on the eve of Mr. Trump’s meeting with Mr. Xi, injected an unpredictable note into an encounter that has been billed mostly as a get-acquainted session for the two leaders.
Mr. Trump made it clear the informal setting would not prevent him from confronting his guest with the chronic imbalances between the United State and China.
“We have been treated unfairly and have made terrible trade deals with China for many, many years,” he said to reporters on Air Force One. “That’s one of the things we are going to be talking about.”
Mr. Xi arrived in Florida on Thursday afternoon, stepping off his Air China flight into the humid air of Palm Beach. On Thursday evening, he attended a formal dinner at Mr. Trump’s Mar-a-Lago estate. A series of meetings were scheduled for Friday morning, followed by a working lunch.
Secretary of State Rex W. Tillerson greeted Mr. Xi and his wife, who walked on a red carpet, flanked by an honor guard carrying flags of both countries. Mr. Trump, who arrived from Washington later, greeted Mr. Xi in an arrival ceremony at the front steps of the estate.
Speaking to reporters afterward, Mr. Tillerson said the president was prepared to demand an “economic relationship that is fair on both sides” and said the chief goal of the nation’s trade policy would be fashioned after the president’s “America First” credo.
“To that end,” he said, “we will pursue economic engagement with China that prioritizes the economic well-being of the American people.”
For weeks leading up to this meeting, China has served as a kind of proxy for Mr. Trump’s advisers to play out their clashing worldviews. The hard-line contingent — led by the president’s chief strategist, Stephen K. Bannon, and the director of the National Trade Council, Peter Navarro — squared off against the more traditional group, which included two former Goldman Sachs executives, Gary D. Cohn, the director of the National Economic Council, and the Treasury secretary, Steven Mnuchin. Mr. Mnuchin, one official said, has gravitated in recent days toward a tougher line on China.
Mr. Bannon, officials said, pushed hard for the removal of Mr. Quinn, a special assistant for international trade, investment and development.
Mr. Quinn had the support of his boss, Mr. Cohn, a Democrat who has emerged as an influential voice with Mr. Trump on economic policy. But he was unable to save Mr. Quinn, who will return to his previous post with the Office of the United States Trade Representative.
In a conciliatory gesture, the two countries are expected to announce they will continue to hold an annual high-level dialogue on strategic and economic issues, which began during the George W. Bush administration and continued under Mr. Obama, though there has been some talk of elevating the session to the level of Vice President Mike Pence.
Among the sensitive topics that may come up is American concern about the possibility that Chinese investors might seek to purchase the nuclear power business of Westinghouse Electric Co.
Westinghouse, once a symbol of America’s leadership in nuclear energy, was forced to file for bankruptcy in late March, in the face of mounting losses. Though many of its wounds were self-inflicted — a disastrous deal for a construction business proved too costly — broad market and industry forces have also changed the economic calculus for nuclear energy.
American officials are profoundly concerned about the potential national security implications of a purchase of Westinghouse by interests with ties to the Chinese government, including the danger that a sale could deliver sensitive nuclear secrets to that nation.
A White House official said Thursday that the administration is watching the potential sale closely but declined to comment on options that the United States government might have to block the sale to Chinese interests.
Bloomberg News first reported about the government’s concern about the sale. Discussions about the issue are underway among top American officials at the Department of Energy, the State Department and the Treasury Department.
Even before the bankruptcy, Westinghouse’s Japanese parent was already moving away from the business of building nuclear power plants, focusing instead on maintaining existing reactors and developing reactors.
It follows a broad pattern in the business, as big companies reassess the viability of nuclear and the field of players shrinks. General Electric has pared its nuclear operations, while the French builder Areva is going through a major restructuring.
China has been moving to fill the void, as it increasingly develops its nuclear abilities and pushes homegrown players to look for opportunities beyond their borders. But China’s increasing presence in nuclear energy has raised security concerns in some countries.