CHICAGO — Gov. Bruce Rauner, the newly elected Republican who has often criticized public sector unions, took his first step toward curbing their power on Monday by announcing an executive order that would bar unions from requiring all state workers to pay the equivalent of dues.

Mr. Rauner, who faces a Democratic-controlled legislature with strong ties to labor, took the unilateral step saying that he believed those fees violate the United States Constitution.

“Forced union dues are a critical cog in the corrupt bargain that is crushing taxpayers,” Mr. Rauner said. “An employee who is forced to pay unfair share dues is being forced to fund political activity with which they disagree. That is a clear violation of First Amendment rights — and something that, as governor, I am duty bound to correct.”

Mr. Rauner, a former private equity manager who became the state’s first Republican governor in more than a decade, is following other Republican governors in the Midwest who have aggressively taken on public sector unions in recent years.