(CNN) Illinois Gov. J.B. Pritzker said Tuesday that he has "given up" on receiving federal assistance to help combat the novel coronavirus pandemic , saying instead that his state is "doing what we need to do despite" President Donald Trump.

"We have gotten very little help from the federal government. It's fine. I've given up on any promises that have been made," Pritzker, a Democrat, told CNN's Erin Burnett on "OutFront." "I hope something will get delivered from the federal government, but I don't expect it anymore."

His comments follow the President's statement earlier Tuesday at a White House news conference that governors "are supposed to do testing" for Covid-19, despite many state leaders saying they need federal assistance to do so. The lack of testing has been a point of contention between governors and the federal government, as the number of coronavirus cases increases.

The Trump administration has faced widespread criticism for the lack of a nationwide testing system to identify those infected with the coronavirus and track the spread of the outbreak. While testing has ramped up in recent weeks, the lack of an aggressive regimen early in the outbreak led to accusations that the government missed a chance to reduce the speed and scale of the pandemic in the United States.

For Illinois, Pritzker said Tuesday, "the President at this point is near irrelevant when it comes to this question of testing."

Pritzker, an outspoken state leader during the pandemic, has expressed frustration before over how Trump has handled the federal response to the outbreak. He previously said he had told the Trump administration his state needed 4,000 ventilators , and he told CNN's Jake Tapper that the President's inaction on states' requests had created a "a Wild West" environment for procuring much-needed medical supplies.

The US now leads the world in the number of reported coronavirus cases, as more than 97% of the US population is under stay-at-home or shelter-in-place orders . Many state and local officials have warned that far more diagnostic and antibody testing -- on the order of millions per day -- is needed so that states can safely relax those distancing precautions and isolate those who are infected.

Acknowledging the desire to "move past" the virus, Pritzker cautioned that "the preconditions just aren't there yet" to relax the social-distancing measures aimed at mitigating the pandemic.

"I know we all want this to end soon. We really do. But I'm not going to risk having another spike come and having more people hospitalized, having our hospital and health systems overwhelmed and more people dying," he said.

"So we're going to do this very gradually. Very carefully. I want people to get back to work just as much as the President does. But we've got to be not expeditious about it, but very careful and rely most importantly on the science."