By Julia-Ambra Verlaine

One of Wall Street's biggest employers is calling its trading staff back to the office.

JPMorgan Chase & Co. executives told senior employees of the bank's giant sales and trading operation that they and their teams must return to the office by Sept. 21, according to people familiar with the matter.

Trading chief Troy Rohrbaugh and Marc Badrichani, the bank's global head of sales and research, delivered the message in conference calls Wednesday morning, the people said. The two executives said employees with child-care issues and medical conditions that make them more vulnerable to coronavirus complications can continue working from home, the people added.

The calls were addressed to managing directors and some executive directors, the unit's most senior managers, the people said.

Companies that have allowed employees to work from home this year face a delicate task in calling them back. College towns that have reopened for in-person classes have been beset by coronavirus outbreaks. Employers have struggled with problems like how to enforce mask-wearing mandates, and they say they are navigating unprecedented circumstances with patchwork guidelines.

Still, Amazon.com Inc. said last month that it would expand its physical offices in New York and other cities, signaling its belief in the long-term viability of office work.

"We all recognize that the city's future depends on people coming back to the office," said Kathryn Wylde, CEO of Partnership for New York City, a business organization.

Like most New York City office workers, Wall Street traders and bankers scattered to the winds when coronavirus shut down the city in March. Workers began trickling back into their skyscrapers in June, when the city began reopening, but financial firms largely haven't ordered employees to return en masse.

Before JPMorgan sent employees home in mid-March, a coronavirus outbreak sickened more than a dozen people on the fifth floor of its Madison Avenue office. By fully reopening its trading floor, the bank is sending a message to its employees -- and its competitors -- that it is now safe to return.

Going remote was hard for Wall Street. Trading floors thrive on shoptalk, banter and elaborate technology setups. Clannish teams share takeout meals during long hours spent in tight spaces. When markets were melting down in the pandemic's early days, veteran traders and their bosses worried that their home offices weren't equipped to handle the chaos.

Yet for many bank executives, the past six months have proved what they previously thought was impossible: Trading could take place seamlessly outside the walls of densely populated office towers. Remote-login systems worked and home internet connections didn't fail. Goldman Sachs Group Inc. kept Zoom channels open all day to bring the trading floor, with its noisy squawk boxes and hoots, to employees' home offices.

JPMorgan, which is building a new skyscraper in Midtown Manhattan, has been more aggressive than some of its peers about bringing workers back to the office.

JPMorgan employees said they have mixed feelings about returning to the office full-time, with some citing concerns around the commute and a potential second wave of the virus. Others are eager to return rather than work from cramped, at-home quarters. Many junior staff have been working at headquarters and backup sites throughout the summer.

It has been a busy season. While the coronavirus has decimated many U.S. businesses, leaving millions of Americans unemployed, the stock market has roared and some Wall Street firms have notched record quarters, widening the gap between the real economy and financial markets.

Wild markets sent investment banking and trading revenue to an eight-year high in the first half of 2020, according to industry research group Coalition, which compiled data from the 12 largest global investment-banking firms.

The strong showing has some on Wall Street questioning the need to come back to the office at all. Many of the technology companies that poach Wall Street's top talent have made remote work permanent. In response, some banks are following suit -- at least for part of the week.

Deutsche Bank AG sales and trading staffers are making bespoke arrangements to work from home two or three days a week even after the pandemic ends, according to people familiar with the matter.

In a note to employees Tuesday, UBS Group AG co-presidents of the investment bank, Piero Novelli and Robert Karofsky, said "flexibility and remote working" are here to stay, according to a readout of the memo. "We expect you to return at your own pace and when you feel comfortable," they wrote.

American Express Co. opened its New York headquarters to nonessential employees this week, limiting the return to 10% of its workforce. The company also said that the return to the office was optional for most employees and that its optional work from home policy would be extended globally to June 30.

Chief Executive Stephen Squeri said in an employee memo that the company recognized that many workers are planning for an "uncertain academic year that may involve remote learning" or they may be caring for elderly relatives. "In addition, many of you rely on public transportation to commute to work and may not feel comfortable using mass transit for the time being," the statement said.

At JPMorgan, trading revenue across fixed-income and equities surged 79% year-over-year to $9.7 billion in the second quarter, a record.

Messrs. Rohrbaugh and Badrichani told employees that camaraderie would suffer and junior staffers wouldn't get the training they need if trading staff remained at home full-time, according to people familiar with the matter.

Still, employees are wary. To calm their nerves and prepare them for the transition, JPMorgan recently pushed out a mandatory training program explaining the new office rules, the people said. Animated figures wearing masks outline hand-washing procedures and hallway etiquette.

Peter Grant contributed to this article.

Write to Julia-Ambra Verlaine at Julia.Verlaine@wsj.com