Prince George’s County Executive Rushern L. Baker III issued his first veto Thursday, rejecting a bill that would allow a government examiner to make binding rulings in condominium and homeowner association disputes.

The measure, which was introduced by council member Leslie E. Johnson (D-Mitchellville) and approved June 14 by a unanimous County Council vote, is unaffordable, Baker said in a veto message to the council late Thursday.

Thursday was the final day Baker (D) could veto the legislation. The council could try to override the veto before going on summer recess this month.

“Overall I am in favor of the concept of this legislation. However, after careful review of this unfunded mandate, it is clear that it would further jeopardize the county’s already strained budget,” Baker wrote. He said the proposal might duplicate existing services.

The bill’s passage was Johnson’s only significant legislative triumph, but it is unclear whether she will be in a position to lobby to overturn the veto or whether other council members might take up the fight for the bill.

Johnson, a lawyer and former administrative law judge who is awaiting sentencing in a federal corruption case, left the council dais Tuesday shortly before her colleagues called for her immediate resignation. They reassigned her staff and said they would ask her to turn in her cellphone, county car, parking pass and computer. A formal letter requesting the material was sent by certified mail Thursday, council spokeswoman Karen Campbell said in an e-mail.

Johnson pleaded guilty last week to destroying evidence in a wide-ranging federal probe that ensnared her and her husband, former county executive Jack B. Johnson (D). The couple were arrested Nov. 12, 10 days after Leslie Johnson was elected.

Jack Johnson, 62, who pleaded guilty last month to accepting more than $400,000 in bribes, is to be sentenced Sept. 15. Leslie Johnson, 59, is to be sentenced Oct. 15. Initially, Johnson said she would serve on the council until then, which she would be allowed to do by law. But on Tuesday, she said she would step down July 31. Both Johnsons face likely jail time.

The plea deal did not play a role in Baker’s decision to veto the bill, a spokesman said. Baker has repeatedly said the county must cut costs and limit new expenditures.

Baker said in his veto message that the county could seek state permission to charge for the mediation system.

“We comprehensively explored all aspects of this issue, and I would be more than willing to examine it in the future,” Baker wrote. “I feel that vetoing this bill is the most prudent course of action.”

Baker, who inherited a $77 million budget deficit from predecessor Jack Johnson, has had to contend with a tight budget for county services and schools. The $2.7 billion budget, approved in May by the council, was essentially flat over last year’s.

Baker has said he wants to focus spending on improving schools, attracting new businesses and cutting crime. Like most jurisdictions across the Washington region, Prince George’s is facing dwindling revenue and lower-than-expected tax collections.

Council Chairman Ingrid M. Turner (D-Bowie) said she understood Baker’s budgetary concerns. “We are concerned with those, too,” she said. “We were led to believe that the impact was minimal; perhaps he has new information. We look forward to working with him on this.”