WASHINGTON — During a recent marathon session in the House, two Republican lawmakers from Georgia sat in full view of television cameras. Neither was wearing a mask.

It was the latest act of defiance by the pair, Representatives Marjorie Taylor Greene and Andrew Clyde, against a rule requiring legislators to wear masks on the House floor. Most Republican lawmakers, however grudgingly, have complied with the mandate, which can carry fines that quickly add up to hefty amounts. But Ms. Greene and Mr. Clyde have repeatedly, and proudly, flouted it.

To date, the two have incurred more than $100,000 combined in fines, which are taken directly from their paychecks.

A resolution approved by the House in January says that members will be fined $500 the first time they fail to wear a mask on the House floor, and $2,500 for subsequent violations. The House Ethics Committee notes each fine in a news release, but Ms. Greene’s and Mr. Clyde’s violations were so numerous that the panel began announcing theirs in bunches.

Ms. Greene, who has said she is unvaccinated, called the mask requirement “communist,” “tyrannical” and “authoritarian.”

“The American people have had enough and are standing up against these outrageous and unconstitutional policies,” she said in a statement.

Ms. Greene has been fined more than 30 times for violating the mask rules, accumulating more than $80,000 in penalties, according to her office. She was fined five days in a row during one stretch this fall.

Only 20 of Ms. Greene’s fines, totaling nearly $50,000, have been announced by the Ethics Committee. (House procedures and appeals can delay announcements by up to two months.)

Mr. Clyde has been fined at least 14 times for violating the mask rule, accruing at least $30,000 in penalties.

In contesting his fines, Mr. Clyde has accused the House and the sergeant-at-arms, who enforces the penalties, of a “deeply troubling” practice of “selective enforcement.”

Representative Thomas Massie, a Kentucky Republican who has also been fined, suggested that Mr. Clyde had found a way around paying the penalties. Mr. Massie told CNN that Mr. Clyde had changed his payroll withholdings so that he was paid only $1 a month.

A spokeswoman for Mr. Clyde did not respond to a request for comment.

Other Republicans who have been fined at least once for not wearing a mask on the House floor include Bob Good of Virginia, Brian Mast of Florida, Mary Miller of Illinois, Beth Van Duyne of Texas, Chip Roy of Texas, Ralph Norman of South Carolina and Mariannette Miller-Meeks of Iowa.

Mr. Massie, Ms. Greene and Mr. Norman have filed a federal lawsuit in Washington against Speaker Nancy Pelosi, seeking a judge’s order to strike down the fines as unconstitutional. The suit accuses Ms. Pelosi of using the mandate “as a cudgel” to dock the pay of her “political opponents.”

It argues that the House may fine members for disorderly behavior, but that the Republicans do not believe refusing to wear a mask falls into that category.

“Merely entering the House chamber without a mask,” the suit says, “did not constitute ‘disorderly behavior’ because it did not disrupt the House’s operations or good order, nor is it otherwise unlawful conduct.”

Ms. Pelosi has said the mask rule helps protect lawmakers and staff members from a “terrible epidemic that has caused suffering and death on a scale not seen in this country since the 1918 influenza pandemic.”

In a court filing, Douglas N. Letter, the House’s general counsel, noted that one member of Congress, Representative Ron Wright, Republican of Texas, and a representative-elect, Luke Letlow, Republican of Louisiana, died after contracting the virus.

Mr. Letter said that issuing fines for refusing to wear a mask fell squarely within the House’s constitutional powers to “govern its own chamber proceedings and to discipline its own members.”

“This is particularly true here,” he wrote, “where the resolution at issue is designed to protect the health of members and staff in the place where all full House debates and votes take place.”

Those arguments appeared to find support in court this month, as a federal judge expressed skepticism about the merits of the suit.

A House rule requiring members to pass through a metal detector before entering the chamber has also resulted in violations.

That rule was enacted after a pro-Trump mob attacked the Capitol on Jan. 6 and Ms. Pelosi pushed for enhanced security. A first violation carries a $5,000 fine, followed by $10,000 for subsequent violations.

Mr. Clyde and seven other Republicans have been fined for violating the metal detector rule, as was Representative James E. Clyburn, Democrat of South Carolina.

The penalties against Mr. Clyburn and five of the Republicans were dismissed on appeal.

But the fines against Mr. Clyde — two totaling $15,000 — and the other Republicans, Louie Gohmert of Texas and Lloyd Smucker of Pennsylvania, were upheld.