But the Chinese have indicated that they will pull out of the talks if Mr. Trump follows through on his threat to impose tariffs on another $200 billion in Chinese goods, according to a person familiar with the matter. Mr. Trump has told advisers that he wants to move ahead with the new round of tariffs and an announcement could come as early as this week, another person familiar with the discussions said.
That continues a frustrating trend for America's financial titans: Even as they win tax cuts and regulatory rollbacks from the Trump administration and the Republican-controlled Congress, they appear to be able to do little to stop the trade war.
"What's really surprising is that the connections that used to work, the formula that used to work, just don't work at this point," said Marshall W. Meyer, an emeritus professor of management at the Wharton School of Business.
Wall Street has long gambled that helping China would pay off. China has been slow to open its vast but tightly controlled financial markets, and Wall Street banks hope to get more business advising Chinese companies on acquisitions in the United States, lending money and selling financial services. Pressure from the Trump administration is now bearing fruit as China has begun to open its financial markets to foreign banks.
A worsening trade war could stymie that progress, and it hurt other foreign businesses as well. Lou Jiwei, China's former finance minister, said in a speech on Sunday that China could block exports of crucial components for Western supply chains if the trade war continued. Such a move would disrupt American businesses but would likely accelerate corporate efforts to shift factories away from China, and current Chinese officials haven't publicly discussed such a dramatic step.
The financial sector's arguments have often found a sympathetic ear in Washington. Over the past two decades, China has emerged as a major global economic growth driver and as an important customer for many American companies, including Apple, Qualcomm and General Motors.
But the Trump administration's trade hawks have so far prevailed against Wall Street-friendly voices of trade moderation, such as Mr. Mnuchin, a onetime Goldman Sachs executive. That is partly because the trade war hasn't shown President Trump much downside. His stance has won support from both parties. The United States economy shows few signs of trade-war damage, and markets continue to rise.
Even if Republicans lose Congress in November's elections, the trade war will probably continue, said Robert B. Zoellick, a former United States trade representative. Only a slump in the markets might make him reconsider, Mr. Zoellick said.
"I don't think that's going to affect Trump," Mr. Zoellick said about November's elections. "Markets could."
Relations between President Trump and Wall Street are complicated. Last year's tax bill greatly favored big financial companies, but some financial executives have clashed openly with Mr. Trump.
JPMorgan's chief executive, Jamie Dimon, a onetime informal adviser to Mr. Trump, said last Wednesday in a speech that "I'm smarter than he is" and that unlike Mr. Trump's, his personal wealth "wasn't a gift from Daddy." Mr. Trump the next day called Mr. Dimon a "nervous mess," and Mr. Dimon has since said he shouldn't have made the remarks. Others, like Morgan Stanley's chief, James Gorman, and the chief executive of Goldman Sachs, Lloyd C. Blankfein, opposed Trump policies like his original travel and immigration ban.
In the past, Wall Street was an effective advocate. In the late 1990s, when China's effort to lower trade barriers faced tough political opposition, China flew its premier, Zhu Rongji, to New York to meet directly with financial and business leaders. Senior leaders of Goldman Sachs and the American International Group, the big financial conglomerate, urged President Clinton to strike a deal. He did, and China joined the World Trade Organization in 2001.
Wall Street also discouraged the United States from formally accusing China of manipulating its currency. Both President Bush and President Obama vowed to get tough on China's longstanding efforts to weaken the value of its currency to help its importers. Wall Street banks urged them to reconsider. Both ultimately backed down. (President Trump has also threatened to label China a currency manipulator, though the currency has strengthened considerably in recent years. Business leaders and some members of his administration have discouraged him from acting.)
The Wall Street influence ran deep. Robert E. Rubin, a Wall Street veteran, served as Treasury secretary under President Clinton and helped forge the consensus within the Clinton administration on how to bring China into the World Trade Organization. Henry M. Paulson Jr., a former Goldman Sachs executive with a high profile in China, served as President Bush's Treasury secretary.
Wall Street figures have cultivated China connections in other ways. Mr. Schwarzman has raised more than $500 million to build a scholarship program in his name at China's prestigious Tsinghua University. Goldman Sachs last year said it would help China's sovereign wealth fund put $5 billion into acquiring stakes in American businesses.
Mr. Schwarzman is working behind the scenes to get China and the United States talking again. He urged American officials to invite their Chinese counterparts to resume talks, according to the people familiar with the discussions.
Last week, Mr. Mnuchin issued an invitation, which Chinese officials publicly greeted warmly. But Larry Kudlow, President Trump's chief economic adviser and another Wall Street veteran, suggested afterward that China had sought the invitation.
"There's some discussions and information that we've received that the top of the Chinese government wishes to pursue talks," he told Fox News.
The meeting in Beijing on Sunday — organized by Zhou Xiaochuan, China's former central banker, and John Thornton, a former Goldman Sachs president — gave Wall Street a chance to press for more business from China. The bankers were planning to present Wall Street's wish list for more market access, including creating a more transparent process for financial firms to get operating licenses and expanding the services that American bank branches can offer.
Because the meeting was called on short notice, top Wall Street executives didn't attend. Most sent a senior executive, like Franck Petitgas, head of Morgan Stanley's international business; John Waldron, president of Goldman Sachs; and Jon Gray, the No. 2 executive at Blackstone. Officials will pass suggestions to Mr. Liu, Mr. Xi's top economic adviser.
Prospects are good that this type of outreach will help, said Wendy Cutler, a former United States trade negotiator.
"Traditionally there have been these back channels, and one of the reasons why Beijing has put people like Liu He in these senior positions has been because they have such good relationships with Wall Street," said Ms. Cutler, who is vice president of the Asia Society Policy Institute.
"To date, these back channels don't seem to be working in moving this administration towards a negotiated solution."
—Alexandra Stevenson reported from Hong Kong, Kate Kelly from New York and Keith Bradsher from Beijing.