Representative Kevin McCarthy, Republican of California and the minority leader, asked the Supreme Court on Thursday to strike down the proxy voting system adopted by the House of Representatives last year to allow for remote legislating during the pandemic.

Mr. McCarthy’s appeal came after a federal appeals court tossed out a lawsuit he filed against Speaker Nancy Pelosi of California seeking to invalidate the voting system, the first in history to allow members of Congress to cast votes in the House without being physically present.

In that July ruling, a three-judge panel of the U.S. Court of Appeals for the District of Columbia unanimously agreed that courts did not have jurisdiction under the Constitution to wade into the House’s rules and procedures. The decision upheld an earlier ruling by a Federal District Court and was endorsed by judges nominated by Bill Clinton, Barack Obama and Donald J. Trump, suggesting a broad consensus on the issue.

But House Republicans have continued to press the matter despite the setbacks, casting the remote voting rules as a political “power grab” by Democrats designed to pad their razor-thin majority — though 97 Republicans have also adopted the practice in recent months, as remote voting has become a tool of personal and political convenience for lawmakers.

“Although the Constitution allows Congress to write its own rules, those rules cannot violate the Constitution itself,” Mr. McCarthy said in a statement, “including the requirement to actually assemble in person.”

House Democrats implemented the special rules in May 2020, allowing lawmakers who were not present to designate other members as proxies who would cast their votes according to specific instructions. They have argued that the changes are necessary for safety reasons, given the danger of traveling in a pandemic and the need for social distancing. They have also noted that a number of Republican lawmakers have refused to share their vaccination status or wear masks in the crowded rooms of Congress.

It is unclear how long the measure, which was presented as a temporary one, might last.

Republicans, led by Mr. McCarthy, quickly filed suit. They argued that the nation’s founders had intended for Congress to meet in person, and argued that the proxy voting system violated constitutional principles. They have also promised to immediately return to normal voting procedures if they retake the majority next year.

The system, which has also allowed members of Congress for the first time to conduct remote committee hearings and file bills electronically, has been used by lawmakers in both parties for purposes other than its intended one. Some members have used remote voting to save them the hassle of traveling from their districts to Washington, while others have used it to be able to cast a vote while attending political events. And it has served the interests of Speaker Nancy Pelosi, who can ill afford absences in Democratic ranks given her slim majority in the House.