By Mary Wisniewski

CHICAGO (Reuters) - Illinois' comptroller will not implement an anti-union executive order issued by the state's new Republican governor earlier this week, the state's attorney general's office said on Friday.

Leslie Munger, a fellow Republican who was appointed by Governor Bruce Rauner, is following current law in not enforcing Rauner's order to eliminate "fair share" fees for about 6,500 state employees, said a spokeswoman for Illinois Attorney General Lisa Madigan.

The fees are paid by workers who are represented by a union but have chosen not to join.

"We agree with the comptroller's assessment and actions in that fair share fees are applicable under current law," said Natalie Bauer, spokeswoman for Madigan, a Democrat. "Fair share fees are constitutional."

A spokesman for Munger said that the comptroller will defer to Madigan's guidance as it relates to actions "within the scope of her legal authority."

In addition to his order on Monday, Rauner also filed a lawsuit seeking to have the fees declared unconstitutional and wanted them placed in an escrow account during the legal process. The comptroller's office is in charge of paying state bills, including paychecks for workers.

A representative for Rauner was not available for comment.

Union leaders applauded Munger's and Madigan's decision.

"It is gratifying to know that two of our state's constitutional officers are clearly committed to upholding the Constitution," said Roberta Lynch, executive of the American Federation of State, County and Municipal Employees Council 31, the largest public labor union for state workers in Illinois.

Lynch, who has argued that the order is illegal, said that the fact that Munger and Madigan are from different political parties shows it is not a partisan issue.

Rauner, a wealthy investment banker and political neophyte who came into office in January, has been vocal about his opposition to public labor unions.

He has argued that reforms are necessary to heal the state's financial problems. Illinois has a chronic structural budget deficit as well as the lowest credit ratings and the worst-funded pension system among the 50 states.

Rauner said he based his order on a review of the U.S. Supreme Court decision last year in Harris v. Quinn, which found that Illinois law violated the First Amendment by forcing home healthcare aides to involuntarily pay union fees.

(Reporting by Mary Wisniewski; Editing by Susan Heavey)