"We are bringing our country back," Mr Trump said during a visit to a mask-manufacturing factory in Arizona.
New confirmed infections per day in the US currently top 20,000, and daily deaths exceed 1,000.
US health officials warn the virus may spread as businesses begin to reopen.
The US currently has 1.2 million confirmed coronavirus infections and more than 70,000 related deaths, according to Johns Hopkins University.
What did President Trump say?
During a visit to the plant in Phoenix, Mr Trump told journalists: "Mike Pence and the task force have done a great job, but we're now looking at a little bit of a different form, and that form is safety and opening. And we'll have a different group probably set up for that."
The president was asked if it was "mission accomplished", and he said: "No, not at all. The mission accomplished is when it's over."
He told reporters: "We can't keep our country closed for the next five years."
Critics have accused the president of sacrificing Americans' public health by rushing to reopen the US economy ahead of his re-election battle in November.
The president was also asked if White House task force experts Dr Deborah Birx and Dr Anthony Fauci would still be involved in efforts to address the coronavirus.
"They will be and so will other doctors and so will other experts in the field," the president answered.