"The Dems think it would be bad for them politically if U.S. schools open before the November Election, but is important for the children & families," Trump tweeted, referring to Democrats. "May cut off funding if not open!"
Trump did not provide evidence that Democrats "think it would be bad for them politically" if schools reopened. He sees reopening schools to help parents go back to work as critical to an economic comeback -- and his reelection effort.
On Tuesday, Trump threatened to "put pressure" on governors who resisted.
Public health experts have generally said that schools can be reopened if precautions are taken but warned rising cases in some states could complicate any plans.
Most control of -- and funding for -- schools in the United States comes from state and local governments.
Asked about Trump's funding threat at a news conference later on Wednesday, Vice President Mike Pence, who leads the White House's coronavirus task force, suggested the White House would attempt to tie some money in future coronavirus-related legislation to schools reopening.
“As we work with Congress on the next round of state support, we are going to be looking for ways to give states a strong incentive and an encouragement to get kids back to school," he said in response to a question from ABC News' Jordyn Phelps.
Pence said the federal government was "here to help" and that "we don’t want federal guidance to be a substitute for state and local laws and rules and guidance."
Trump, meanwhile, in another Wednesday tweet attacked the CDC -- a federal agency run by a man he appointed -- for recommendations it had made to help educational institutions reopen.
"I disagree with @CDCgov on their very tough & expensive guidelines for opening schools," Trump wrote. "While they want them open, they are asking schools to do very impractical things. I will be meeting with them!!!"
The CDC's guidelines, which are voluntary, encourage school staff and students "to take everyday preventive actions to prevent the spread of respiratory illnesses" -- like washing hands and staying home while sick.
The agency said that under certain circumstances, large gatherings and field trips should be cancelled, and that if the virus's spread picks up, schools may need to be dismissed for weeks.
Pence said he spoke with Trump and that the president's tweet reflected the president's "leadership" and "desire" for the guidance to not "be a reason why schools don't open."
"I think what the president was saying this morning is that, if there are aspects of the CDC’s recommendations that are prescriptive or that serve to -- as a, as a barrier to kids getting back to school, we want -- we want governors and local officials and education leaders to know that we’re here to work with them, to support the measures they are putting into place," Pence said.
CDC Director Robert Redfield said it would be "disappointing" if people used the guidelines as an excuse for not opening schools and that they were "not meant to be prescriptive."
"I want to make it very clear that it is not the intent of CDC's guidelines is to be used as a rationale to keep schools closed," Redfield said at the news conference. "We are prepared to work with each school, each jurisdiction to help them use the different strategies that we propose that help do this safely so they come up with the optimal strategy for those schools." 121450
He later added that it was "important that we don't react emotionally, but we act based on data."
Redfield said the CDC was "about to put out" what he called "a series of different -- additional guidelines" for the K-12 community and for parents and caregivers. He said they would cover symptom surveillance, the ins and outs of face masks, and systems to "monitor their programs."
In some school districts, classes normally begin as soon as early next month.
"Ultimately it's not a matter of if schools should reopen," DeVos told reporters. "It's simply a matter of how. They must fully open, and they must be fully operational and how that happens is best left to education and community leaders."
ABC News' Elizabeth Thomas and Sophie Tatum contributed reporting.
This report was featured in the Thursday, July 9, 2020, episode of “Start Here,” ABC News’ daily news podcast.
"Start Here" offers a straightforward look at the day's top stories in 20 minutes. Listen for free every weekday on Apple Podcasts, Google Podcasts, Spotify, the ABC News app or wherever you get your podcasts.