President Elect Donald Trump alleges that ‘millions of people’ voted illegally

Separately, officials in three states that gave Mr. Trump his margin of victory this month are gearing up for recounts in the face of heated pushback from Mr. Trump and his advisers.

The Wisconsin Elections Commission will meet Monday to approve a timeline for a recount there after Green Party candidate Jill Stein successfully submitted paperwork last week. In Pennsylvania, the Stein campaign faces a huge organizational hurdle, with state law requiring supporters to file requests in more than 9,000 districts across the state by Monday to force a full recount. And the campaign is still raising funds for a challenge in Michigan, which must be filed by Wednesday.

The proposed recounts are unlikely to significantly alter the results of the hard-fought campaign that saw Mr. Trump prevail despite Mrs. Clinton’s significant lead in the popular vote. Mr. Trump leads in Michigan by nearly 11,000 votes, in Wisconsin by just more than 20,000 and in Pennsylvania by nearly 71,000. Mrs. Clinton would need to prevail in recounts in all three states to win the White House, a margin of more than 100,000 votes—something that even her campaign acknowledges is likely impossible absent evidence of widespread fraud or tampering.

No recount has ever produced such a large swing in votes. Her campaign’s general counsel said Saturday that it hadn’t planned to request a recount but would participate in the process initiated by Ms. Stein to ensure Mrs. Clinton’s interests were represented during the process.

“We do so fully aware that the number of votes separating Donald Trump and Hillary Clinton in the closest of these states—Michigan—well exceeds the largest margin ever overcome in a recount. But regardless of the potential to change the outcome in any of the states, we feel it is important, on principle, to ensure our campaign is legally represented in any court proceedings and represented on the ground in order to monitor the recount process itself,” attorney Marc Elias wrote.

The renewed involvement of Mrs. Clinton in recount efforts sparked a furious reaction from Mr. Trump and other Republicans. In a statement over the weekend, Mr. Trump called the effort “ridiculous,” and a “scam” by Ms. Stein to raise funds and boost her profile.

Speaking Sunday on Fox News, Republican National Committee Chairman Reince Priebus, who will be Mr. Trump’s chief of staff, criticized Mrs. Clinton’s campaign for joining the effort.

“It is a total and complete hypocritical joke that the group of people that thought that they were nervous about President-elect Trump not conceding are the people that are conducting recounts in states where we won by over 68,000 votes,” Mr. Priebus said. “I think the American people know this is a waste of everyone’s time and money.”

Mr. Trump could try to fight the recounts, including going to court in Wisconsin or Pennsylvania. In Michigan, he could file a protest that would be decided by the Board of Elections. His representatives didn’t respond to a question about whether he would exercise those options.

In Wisconsin, state election officials are beginning the process of preparing for a recount that must be completed in the next three weeks. Under a draft timeline that still needs to be approved by the election commission, the recount would begin Thursday and be completed by Dec. 13.

“It will be a significant challenge to complete a statewide recount of nearly 3 million votes in less than two weeks,” wrote two top Wisconsin election officials in a memo Saturday.

In Pennsylvania, Ms. Stein faces a significant barrier to a statewide recount. Under state law, three voters in each election district need to request a recount of that district. There are more than 9,000 such districts across the Keystone State, meaning that Ms. Stein needs to mobilize nearly 30,000 supporters by Monday to force a recount of every vote in the state.

“While the burden of proof is easy—all you have to do is allege some sort of wrongdoing—the organizational burden is a steep one,” said Adam Bonin, a Philadelphia-based election law attorney who works in Democratic politics.

In addition, many of the voting machines in Pennsylvania are digital without paper backups, meaning that new votes are unlikely to be uncovered. Ms. Stein also has the option of going to court to get a judge to approve a recount.