Mr Mueller, who was tasked by Deputy Attorney General Rod Rosenstein with overseeing the Justice Departments inquiry into possible ties between the Trump presidential campaign and Russian operatives, is staffing up his office - and bringing in some prosecutorial heavy-hitters.
Under Trump's order, private industry would have more flexibility and be eligible for registration by the Labor Department.
Assembly Minority Leader Peter Barca says Trump is pulling a "bait and switch" by claiming he cares about workers while cutting resources to train them.
The comments come amid increasing frustration at the White House and among Trump supporters that the investigation will overshadow the president's agenda for months to come.
Trump accepted a challenge earlier this year from a CEO to create 5 million new apprenticeships. Senior administration officials have said Trump was reluctant to spend more federal funds on apprenticeships, so the boost would come from existing money, perhaps from the streamlining process. The president was set to sign the directive on Wednesday after a speech at the Labor Department, but the event was scrapped due to the shooting at a congressional baseball practice.
"If you're really interested in promoting apprenticeship, you have to invest in that skills training", said Mike Rosen, president of the Milwaukee chapter of the American Federation of Teachers union. "Instead apprentices earn while they learn".
But at the Wisconsin event, the president also heard more broadly about vocational education.
"I think some very good numbers are going to be announced, by the way, in the very near future as to GDP", Trump told the press.
Sen. Tammy Baldwin, D-Wis., said Trump's "rhetoric doesn't match the reality" of the budget cuts he's proposing.
"Apprenticeships are going to be a big, big factor in our country", Trump said during his first-ever full Cabinet meeting Monday.
Apprenticeships are few and far between. The executive order addresses the nation's "skills gap" that have left millions of open jobs unfilled. Of the 146 million jobs in the United States, about 0.35 percent - or slightly more than a half-million - were filled by active apprentices in 2016. "Scaling is the big issue", said Robert Lerman, a fellow at the Urban Institute. The program uses $1.2 billion in federal funding provided under the Perkins Career and Technical Education Act passed in 2006, said P-TECH co-founder Stan Litow.
The president was attending a closed fundraiser for Walker later in the day.
Some of President Donald Trump's closest allies - including one of his sons - have begun questioning whether Mueller's wide-ranging probe is becoming too political, as the investigation into Russian meddling in the 2016 election intensifies. "We're here today to celebrate the dignity of work and the greatness of the American worker".