A trade group representing some 2,000 consumer brands has sent a letter to President Biden on Monday asking for clarification about his announcement last week that all companies with more than 100 employees will soon need to require vaccination or weekly testing.

Mr. Biden last week said that the Department of Labor and its Occupational Safety and Health Administration will draft the rules, which will affect some 80 million workers.

But the mandate has raised vexing issues for employers as they deal with the practicalities of vaccination policies, said Geoff Freeman, the president of the trade group, the Consumer Brands Association.

On Monday, Mr. Freeman called on Mr. Biden to “create immediate clarity” about how private businesses should carry out aspects of the White House’s plan to achieve “our shared goal of increased vaccination rates.”

He shared 19 questions that represented a “small sampling” of those raised by the trade group’s members. Among them:

• What proof-of-vaccination documentation will the companies need to collect and will booster shots also be required?

• Must employees be fully vaccinated?

• Will workers who have had the coronavirus still have to be vaccinated or get tested?

• Will the requirements apply only to vaccines that are fully approved by the Food and Drug Administration? (The Pfizer-BioNTech vaccine is currently the only shot with full approval.)

• Who is responsible for vaccination tracking — the government or the individual businesses?

• What are the consequences of falsifying a vaccination status?

Other questions, on testing and other policy details, covered similar ground, touching on how federal guidelines interact with state-level initiatives, who will be responsible for paying for testing and whether waivers would be allowed if employee absences or attrition results in supply chain disruptions.

Also of concern, Mr. Freeman said in an interview, is the slow pace at which government tends to move, compared with the quick decisions that private businesses are used to making. This has been a problem during the pandemic, he said.

“For 19 months, we’ve been working with either the Trump administration or the Biden administration and all of the agencies involved in this,” he said. “And the simple truth is that they have been slow to keep up with the pace of change.”

He added, “All of us want to get to the other side of this thing as quickly as possible. It’s not going to work in this scenario unless an entity like OSHA can move at the pace of the business environment.”

Major trade groups representing the business community have generally been supportive of the mandate, which gives otherwise wary businesses the cover to require inoculation.

The U.S. Chamber of Commerce, the nation’s largest business lobbying group, has said that it “will work to ensure that employers have the resources, guidance and flexibility necessary to ensure the safety of their employees and customers and comply with public health requirements.” Another major business advocacy group, the Business Roundtable, has said it “welcomes” the Biden administration actions.