A federal appeals court on Sunday temporarily blocked a judge’s order requiring Republican senator Lindsey Graham to testify before a Georgia grand jury investigating efforts to overturn the results of the 2020 presidential election in that state.

The judge who ordered Graham’s appearance in front of the grand jury – Leigh Martin May – should determine whether the subpoena requiring the South Carolina senator testify before the panel should be quashed or modified in accordance with the US constitution’s speech or debate clause.

Generally, scholars interpret the clause as shielding federal lawmakers from being compelled to face questioning from law enforcement in certain cases, and Graham had cited the provision in challenging a subpoena calling for him to testify before the Atlanta-based grand jury in question.

May last week had ruled that prosecutors demonstrated “a special need for Mr Graham’s testimony on issues relating to alleged attempts to influence or disrupt the law administration of Georgia’s 2020 elections” despite the senator’s challenge. But Graham, who had been ordered to testify in the grand jury investigation on Tuesday, had indicated he would appeal on May’s ruling to a higher court.

Judges Charles Wilson, Kevin Newsom and Britt Grant of the 11th US circuit court of appeals then ruled on Sunday that it would send the case back to May for her to determine whether Graham’s subpoena should at least be changed.

May should solicit briefs on the issue from both sides on an expedited schedule, and after she rules again, the case would return to the appellate court, Sunday’s order said.

All told, the order almost certainly means it could be a significant while before Graham appears in front of grand jurors – and even then, it may only be in a limited way, University of Richmond law professor Carl Tobias said to the Guardian on Sunday.

Graham drew the grand jury investigation’s interest because he placed two calls to the Georgia’s top election official in 2020 and asked about ways to invalidate certain mail-in votes that helped buoy Joe Biden to victory over Donald Trump in that year’s presidential race.

The senator and prominent Trump supporter is considered a subject – rather than a target – of the investigation being conducted by the grand jury in Atlanta. That panel is weighing the filing of criminal charges against the former Republican president and his allies for their alleged attempts to deny Georgia voters’ rejection of Trump in 2020 amid a desperate effort to keep him in the Oval Office despite Biden’s electoral college victory over him.

Targets of the investigation include Rudy Giuliani, Trump’s former attorney.

The Georgia grand jury investigation has applied considerable legal pressure on Trump, who is also facing a US justice department investigation over his unlawful retention of government documents at his Mar-a-Lago resort as well as an inquiry by New York state officials into his business practices there.

Trump on Sunday went on his Truth Social platform and sought to persuade his followers that his multi-front legal struggle illustrated Democrats’ fear that he would again clinch the Republican presidential nomination for the 2024 election and challenge their leader Biden.

Trump, who as of Sunday had not yet officially declared that he would once more pursue the White House in 2024, added: “I … may just have to [run] again.”