WASHINGTON — In an unusual joint statement on Wednesday, Justices Sonia Sotomayor and Neil M. Gorsuch sought to rebut reports that Justice Gorsuch’s refusal to wear a mask at Supreme Court arguments has created tensions between them.

“Reporting that Justice Sotomayor asked Justice Gorsuch to wear a mask surprised us,” the statement said. “It is false. While we may sometimes disagree about the law, we are warm colleagues and friends.”

A few hours later, Chief Justice John G. Roberts Jr. issued his own statement. “I did not request Justice Gorsuch or any other justice to wear a mask on the bench,” he said.

Since the justices returned this month from their holiday break, all of them started to wear masks in the courtroom except Justice Gorsuch. At the same time, Justice Sotomayor, who has diabetes and had been the only member of the court to wear a mask since the justices returned to the bench in October, started to participate in arguments remotely from her chambers. Justice Sotomayor sits next to Justice Gorsuch on the bench.

The justices’ statements seemed to be primarily directed at a report by Nina Totenberg of NPR on Tuesday attributed to “court sources.” In it, Ms. Totenberg said that Justice Sotomayor “did not feel safe in close proximity to people who were unmasked.”

“Chief Justice John Roberts, understanding that, in some form asked the other justices to mask up,” the report said.

The justices’ statements did not say whether Justice Sotomayor’s absence from the courtroom was a consequence of Justice Gorsuch’s decision not to wear a mask. But Chief Justice Roberts rejected the assertion that he had asked his colleagues to wear masks on the bench.

Later on Wednesday, Ms. Totenberg said in a report addressing the justices’s statements that “NPR stands by its reporting.”

All of the justices are fully vaccinated and have received a booster shot, a court spokeswoman has said.