On a Monday in mid-March, the Wisconsin Republican Party gathered about 50 conservative activists on a Zoom call to train them in how to become poll workers, helping oversee and monitor the casting and counting of votes.

Heavily Democratic areas of the battleground state were a key focus. “Eau Claire, Madison, Milwaukee — that type,” Mike Hoffman, the state party’s election integrity director, said as he ticked off places being targeted.

“We’re keeping a close eye on you,” he recounted telling one city clerk, according to audio recordings of the party’s training sessions obtained by The New York Times.

The Wisconsin training sessions are a small part of an expansive operation announced on Friday by former President Donald J. Trump’s campaign and the Republican National Committee, which plan to dispatch more than 100,000 volunteers and lawyers to monitor and potentially challenge the electoral process in each battleground state. They will focus on every aspect of voting, including mail ballots, voting machines and post-Election Day recounts and audits.

The sprawling effort is rooted in Mr. Trump’s persistent false claims that Democrats cheated to win the 2020 election. His allies have helped turn that belief into Republican doctrine despite the overwhelming conclusion by Democratic and G.O.P. election officials, as well as federal and state judges, that no evidence of widespread fraud exists.

“Democrat tricks from 2020 won’t work this time,” Charlie Spies, the chief counsel of the R.N.C., pledged in a statement announcing the program. “In 2024, we’re going to beat the Democrats at their own game and the R.N.C. legal team will be working tirelessly to ensure that elections officials follow the rules in administering elections.”