The Justice Department has stepped up its criminal investigation into a plan by President Donald J. Trump and his allies to form groups of so-called fraudulent voters in an attempt to keep Mr Trump in power during the 2020 election as federal agents handed out a grand jury of summonses on Wednesday to at least four people linked to plan.

One of those summoned, according to two acquaintances, was Brad Carver, a lawyer and employee of the Republican Party of Georgia, who claimed to be one of Mr. Trump’s voters in the state, which was won by Joseph R. Biden Jr.

Another recipient of the summons is Thomas Lane, an employee who worked on behalf of Mr. Trump’s campaign in Arizona and New Mexico, people said.

A third person, Sean Flynn, an aide to Trump’s campaign in Michigan, also received a summons, according to sources.

A fourth subpoena was issued to David Shaffer, chairman of the Republican Party of Georgia, who also served as a fake voter for Mr. Trump.

Mr Schaefer’s lawyer declined to comment. None of the other three men could be found to comment on the subpoenas.

The issuance of new subpoenas was announced earlier by The Washington Post.

The fake election plan is the focus of one of two known points in a wide-ranging investigation by the Justice Department’s grand jury into Mr Trump’s numerous and interconnected attempts to undermine the election. The other focuses on a wide range of political organizers, White House aides and members of Congress, linked in various ways to Mr Trump’s incendiary speech near the White House, which directly preceded the January 6, 2021, storming of the Capitol.

This latest round of investigative activities by the Justice Department came amid hearings by a high-ranking House of Representatives committee on Jan. 6 on Mr Trump’s efforts to change the outcome of the election.

That comes less than a month after an earlier round of subpoenas by the grand jury revealed that prosecutors were seeking information on any role a group of pro-Trump lawyers may have played in trying to rigged voters. These lawyers include Rudolf W. Giuliani, John Eastman, Boris Epstein, Jenna Ellis, Kenneth Chesebro, James Troupis and Justin Clark. Although the testimony before the House committee of representatives provided evidence of the roles of some of them in the plan, including Mr Giuliani, Mr Eastman and Mr Cesebro, it is not clear what role, if any, some of the others they could play.

The subpoenas, issued by a grand jury in Washington, also sought records and information on other pro-Trump figures such as Bernard B. Kerrick, a former New York City police commissioner and a longtime ally of Mr Giuliani.

Many of the lawyers named in the subpoenas were also mentioned Tuesday during a public hearing in an elected House of Representatives committee examining Mr Trump’s extensive campaign to persuade government officials to help him stay afloat. post.

At the hearing, the committee directly linked Mr. Trump to the plan for the first time, presenting a recorded testimony from Rona McDaniel, chairwoman of the National Republican Committee, in which she described how Mr. Trump called her and called Mr. Eastman on the phone. “To talk about the importance of the RNC in helping the campaign bring together these contingent voters.”

The first subpoenas in the bogus voter inquiry were largely sent to people in key rocking states who almost took part in the plan, but ultimately did not do so for various reasons. This new round of subpoenas appears to be the first time that Trump campaign officials have been involved in the investigation, which marks a small but potentially significant step closer to Mr Trump himself.

Mr. Biden’s plan to create pro-Trump voters in states was one of the earliest and most widespread conspiracies by Mr. Trump and his allies to overturn election results. It was attended by lawyers, government officials, the White House and campaign staff, as well as members of Congress.

The plan was developed as Mr Trump and his allies sought to encourage baseless allegations of widespread election fraud in key rocking states and to persuade government officials to revoke Mr Biden’s certificate of victory. His goal was to have letters about Trump as Vice President Mike Pence oversaw the official certification of the vote in a joint session of Congress on January 6, 2021.

Mr Trump and others close to him have made relentless efforts in the weeks leading up to January 6 to persuade Mr Pence to either count pro-Trump voters and give Mr Trump victory in the Electoral College, or to declare that elections were uncertain as competing voter lists were obtained in several states.

The idea was to buy Mr Trump more time to prosecute his baseless allegations of fraud or potentially send him to the House of Representatives election, where each US delegation will receive one vote. With more delegations controlled by Republicans than Democrats, Mr Trump could have won.

Adam Goldman and Glen Drush contributed to the reporting.