The attorney general for the state of Texas, Ken Paxton, has agreed to apologize and pay $3.3m in taxpayer money to four former staffers who accused him of corruption in 2020, igniting an ongoing FBI investigation of the three-term Republican.

Under terms of a preliminary lawsuit settlement filed on Friday, Paxton made no admission of wrongdoing to accusations of bribery and abuse of office, which he has denied for years and called politically motivated.

But Paxton did commit to making a remarkable public apology toward some of his formerly trusted advisers whom he fired or forced out after they reported him to the FBI. He called them “rogue employees” after they accused Paxton of misusing his office to help one of his campaign contributors, who also employed a woman with whom the attorney general acknowledged having an extramarital affair.

Both sides signed a mediated agreement that was filed in the Texas supreme court and will be followed by a longer, formalized settlement.

“Attorney general Ken Paxton accepts that plaintiffs acted in a manner that they thought was right and apologizes for referring to them as ‘rogue employees’,” the final settlement must state, according to court records.

In all, eight members of Paxton’s senior staff joined in the extraordinary revolt in 2020, and they either resigned or were fired. The attorney general said he settled with the four who sued under Texas’s whistleblower law to put to rest “this unfortunate sideshow”.

“I have chosen this path to save taxpayer dollars and ensure my third term as attorney general is unburdened by unnecessary distractions,” Paxton said in a statement.

The $3.3m payout would not come from Paxton’s own pocket but from state funds, which means it would still require approval by the Republican-controlled Texas legislature.

Settlement of the case, which Paxton’s office fought in court for years, means he will avoid sitting for a civil deposition at a time when a corruption investigation by federal agents and prosecutors remains open. In turn, the attorney general’s office agreed to remove an October 2020 news release from its website that decries Paxton’s accusers and to issue the statement of contrition to former staffers David Maxwell, Ryan Vassar, Mark Penley and James Blake Brickman.

The settlement also prevents Paxton from seeking the withdrawal of a 2021 appeals court ruling that state whistleblower law applies to the attorney general. But it does not include any provisions limiting the ability of Paxton’s accusers to make public statements or cooperate with federal investigators.

The deal comes more than two years after Paxton’s staff accused him of misusing his office to help Austin real estate developer Nate Paul, whose business was also under federal investigation. The allegations centered on Paxton hiring an outside lawyer to investigate Paul’s claims of misconduct by the FBI.

Paxton and Paul have broadly denied wrongdoing and neither has been charged with a federal crime.

The investigation, accusations and a separate 2015 securities fraud indictment for which Paxton has yet to face trial have done little to hurt him politically. He easily defeated challenger George P Bush in a contested GOP primary last spring, went on to decisively beat his Democratic opponent and secure a third term in November and has filed a steady stream of legal challenges against the Joe Biden White House.

While swearing in Paxton to another four years on the job last month, Texas’s Republican governor, Greg Abbott, described it as an easy call during the midterm elections to keep backing him.

“I supported Ken Paxton because I thought the way he was running the attorney general’s office was the right way to run the attorney general’s office,” Abbott said.