“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 in Baltimore, Maryland, which is tracking the pandemic.
During a visit to the plant in Phoenix after weeks holed up at the White House, 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 – who wore safety goggles but no face mask during his tour of the facility – was asked if it was “mission accomplished”, and he said: “No, not at all. The mission accomplished is when it’s over.”
Critics have accused the president of sacrificing Americans’ public health in his eagerness to reopen the US economy ahead of his re-election battle in November.
In Arizona on Tuesday, Mr Trump said that Democrats were hoping his coronavirus policy would fail “so they can win the election”.
Acknowledging a human cost to the plans, Mr Trump told reporters: “I’m not saying anything is perfect, and yes, will some people be affected? Yes.
“Will some people be affected badly? Yes. But we have to get our country open and we have to get it open soon.”
However, it will be up to individual states to determine how they reopen.
Some Democratic governors in badly hit states have been cautious, calling for more testing and other safeguards before easing lockdowns. Other states, many led by Republicans in the south and mid-west, have already begun lifting restrictions.
The task force was set up on 29 January. Mr Pence became its chairman four weeks later and its members include more than 20 experts and leading administration officials. The White House said the task force’s duty was to “lead the administration’s efforts to monitor, contain and mitigate the spread of the virus” and provide the public with information.
Mr Trump’s once-daily task force briefings became increasingly scarce after he was widely condemned by the medical community for pondering at the podium last month whether injecting bleach into people might kill the virus.
Dr Deborah Birx has been the task force’s response co-ordinator. The president was asked on Tuesday whether she and another high-profile member, 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 said.