Liberal advocacy groups called this week for the Senate Judiciary Committee to launch an investigation into Justice Samuel A. Alito Jr. over his wife flying flags that critics say were connected to the Capitol riot on Jan. 6, 2021.

More than two dozen liberal groups — led by Demand Justice — say they want Congress to pass legislation imposing an ethics code on the high court and want to see Justice Alito recuse from cases related to the 2020 election.

“We request that as Chairman you investigate and issue findings on Justice Alito’s conduct as it relates to existing federal law, ethical standards, and the integrity of our judicial system,” read the letter addressed to Senate Majority Whip Richard J. Durbin, Illinois Democrat and chairman of the Judiciary Committee.

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It was sent to the Illinois Democrat on Wednesday, the same day Justice Alito told lawmakers he would not recuse from any case based on their accusations of inappropriate flag flying.

Mr. Durbin requested Justice Alito recuse himself from cases related to the Capitol riot over flying an upside-down American flag outside his Alexandria, Virginia, home days after the violent protest.

He also came under scrutiny for flying an “Appeal to Heaven” flag outside his New Jersey residence in 2023, with critics saying Jan. 6 rioters carried the same flag.

Justice Alito said the flying of an upside-down American flag and “An Appeal to Heaven” pennant at his home were his wife’s decisions and that he’s not biased in any dispute.

“My wife is fond of flying flags. I am not. My wife was solely responsible for having flagpoles put up at our residence and our vacation home and has flown a wide variety of flags over the years,” he said in his letter to Mr. Durbin earlier this week.

“My wife is an independently minded private citizen. She makes her own decisions, and I honor her right to do so,” he added. “A reasonable person who is not motivated by political or ideological considerations or a desire to affect the outcome of Supreme Court cases would conclude that this event does not meet the applicable standard for recusal. I am therefore duty bound to reject your recusal request.”

According to Politico, a spokesperson for Mr. Durbin responded to the request from liberal groups to probe Justice Alito by saying his committee has already been doing the research, saying “the Committee has been conducting a thorough investigation into years of ethical lapses by some justices on the Supreme Court.”

The spokesperson added that Mr. Durbin “will continue to pursue what the American people are demanding: accountability, transparency, and an enforceable code of conduct for Supreme Court justices.”

Justice Alito’s letter came after The New York Times reported that he had flown two flags outside his homes.

In his letter to members of Congress, Justice Alito noted that he didn’t know of a connection between the “Stop the Steal Movement” that led to the Capitol riot and the “Appeal to Heaven” flag.

Democratic lawmakers have called each flying a public display of political activity, which would run afoul of judicial ethics. One House Democrat introduced a censure resolution that demands that the justice recuse himself from any case related to the 2020 election.

The calls for recusal come as the high court is weighing two major disputes this term over whether Mr. Trump is immune from charges stemming from his contest of the 2020 election results and another dispute over an obstruction charge facing hundreds of Jan. 6 defendants, including Mr. Trump.

Those opinions are expected to come by the end of June.

Mr. Durbin also called for a meeting with Chief Justice John G. Roberts Jr. to discuss ethics concerns but on Thursday, the chief justice declined the meeting, saying it would be improper to meet with lawmakers from one political party.

Maggie Jo Buchanan, managing director for Demand Justice, said that was further evidence of the need for a probe by Mr. Durbin’s committee into the high court.

“Chief Justice John Roberts’s unwillingness to even meet with Senators [Sheldon] Whitehouse and Durbin about the deeply concerning actions of Justice Alito is not only disturbing, but serves as further evidence that the Senate Judiciary Committee must immediately launch a full investigation. While Republican leaders may continue to stonewall meaningful ethics reform, Sen. Durbin must not shy away from holding this Supreme Court accountable to the American people,” she said.