A battle to move the Georgia racketeering case against Donald J. Trump and his allies to federal court began in earnest on Monday, when lawyers for Mark Meadows, a former White House chief of staff, made their arguments in favor of a move before a federal judge in Atlanta.

The hearing kicked off the first major legal fight since an indictment was filed in the case brought by Fani T. Willis, the district attorney in Fulton County, Ga. The indictment charges Mr. Trump and 18 allies with interfering in the 2020 presidential election in the state. Mr. Meadows is one of several defendants in the case who are trying to move it to federal court, and any decision could apply to all 19 of them.

If the effort succeeds, it could benefit the Trump side by broadening the jury pool beyond Fulton County into outlying counties where the former president has somewhat more support.

It could also slow down at least some of the proceedings. If the case remains in state court, three of the defendants are likely to face trial starting in October. Kenneth Chesebro has already been granted an early trial, a right afforded under Georgia law, and Sidney Powell has sought the same. A lawyer for John Eastman, another defendant, has said he, too, will seek a speedy trial.

Removing a case to federal court requires persuading a judge that the actions under scrutiny were carried out by federal officers as part of their official business. Earlier this year, Mr. Trump failed in his attempt to move a New York State criminal case against him to federal court; his argument in that case was seen as particularly tenuous.

Presiding over the hearing on Mr. Meadows’s motion Monday was Judge Steve C. Jones of United States District Court in Atlanta. Last week, Judge Jones blocked Mr. Meadows’s attempt to avoid being booked at the Fulton County jail as the other defendants in the case were. The judge ruled that the law was clear that “state court proceedings continue” until a decision has been reached on removal.

The next step for the case in state court came on Monday. when the judge, Scott McAfee, scheduled arraignments of Mr. Trump and the other defendants for Sept. 6. It is possible that some or all of the arraignments will not be conducted in person, given the heightened security requirements involving a former president.

For the next few weeks at least, the case will be wrangled by two different judges working in courthouses a few blocks apart in downtown Atlanta. Judge McAfee, of Fulton County Superior Court, is an appointee of Georgia’s Republican governor, Brian Kemp, and a member of the conservative Federalist Society, though he also once worked for Ms. Willis and is well regarded by many lawyers on both sides of the case.

Judge Jones is an Obama appointee to the federal bench who has been moving quickly regarding the removal question. In 2019, he upheld Georgia’s purge of nearly 100,000 names from its voter rolls, over the objections of liberal activists. In 2020, he blocked a six-week abortion ban from taking effect in the state.

The Georgia case is the fourth criminal indictment of Mr. Trump this year. In March, he was indicted in Manhattan on state charges stemming from hush money paid to a pornographic film actress. He also has been indicted in two federal cases — one in Washington, related to his efforts to overturn the 2020 election, the other in Florida over his handling of classified government documents after leaving office.