Justice Brett Kavanaugh said he is "hopeful" the Supreme Court may soon act on its own to address "perceived ethics issues" as some Democratic lawmakers are pushing their own legislation to rein in the court.

Kavanaugh made his comments on Thursday during a conference of judges and lawyers after he was asked by Judge Stephanie Dawkins Davis of the U.S. Court of Appeals for the 6th Circuit about the perception of ethics matters on the Supreme Court.

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"The chief justice spoke about that in May and said that we're continuing to work on those issues and that is accurate, we are continuing to work on those issues," Kavanaugh said, referring to a speech by Chief Justice John Roberts in May. "And I'm hopeful that there will be some concrete steps taken soon on that."

Kavanaugh's comments come days after Sen. Sheldon Whitehouse (D-RI) called on Roberts to investigate Justice Samuel Alito, who recently pushed back on the notion that Congress could police ethical behavior among the nine justices.

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Whitehouse, who is seeking to pass legislation to enforce ethics on the high court, alleged Alito was improperly opining on matters related to congressional duties when the justice dismissed the notion that Congress could pass such a bill during a July interview with the Wall Street Journal.

This is a developing story and will be updated.