Gov. Scott Walker of Wisconsin said on Monday that he wanted to eliminate the state’s Government Accountability Board, a nonpartisan agency that oversees elections, ethics, campaign finance and lobbying.

In 2012, the board voted unanimously to approve an election to recall Mr. Walker, the first governor in the state’s history to face such a challenge, and it later authorized an investigation into allegations of violations by the governor’s campaign in that election.

Mr. Walker would replace the board with “something completely new that is truly accountable to the people of the state of Wisconsin,” he told reporters after a bill-signing ceremony.