Speaking at a press conference on Wednesday, Pelosi, D-Calif., said Trump should implement the measure to increase the production of personal protective equipment and testing equipment to allow schools and businesses to reopen safely.
"If we want to open our economy and now if we want to open our schools, we have to have the testing, we have to have the judgment and therefore we need the equipment and we also need the PPE," she said.
She also said the expansion of expiring unemployment benefits may depend on the size of direct payments sent to Americans in the next COVID-19 relief bill.
Pelosi said Democrats would look to work with Republicans to determine how much they are willing to offer in direct payments, referring to the "three pillars" of the $3 trillion HEROES Act passed by the House in May.
"That pillar is about putting money into the pockets of the American people. One piece of it is unemployment insurance and the benefit you are talking about and another part of it is how we put direct payments into the families," said Pelosi. "So we'll see what the entire package looks like."
The HEROES Act would provide a second round of direct payments of up to $1,200 for individuals and $2,400 for joint filers but Senate Republican Leader Mitch McConnell has suggested only distributing the funds to people who earn less than $40,000 a year, which Pelosi has challenged.
"I think there are many families depending on size of family and so many different things, that the $40,000 would have to be explained justified and the rest," she said last week. "But I think families making over $40,000 probably need assistance. Again, just depending on their family situation."
McConnell on Wednesday said the next phase of coronavirus relief will focus on providing funding to schools as they prepare to open amid surging cases in some parts of the country.
"There's going to be a heavy emphasis in the bill I'm going to unfold next week on education. I know it will be costly," he said. "We need to find a way to safely get back to work, and we feel, I feel, like the federal government will have to play a financial role in helping to make that possible."
McConnell, like Trump and much of his administration, asserted that it is important for children to return to in-person instruction even though some school districts, including California's Los Angeles and San Diego districts, have already announced plans to begin with online-only instruction.
"We can't have a normal country unless kids are in school," he said. "And of course, that has an impact on jobs because kids and school and jobs are interconnected in every single way. Because it affects both parents to get back to work if the kids are home."