Sen. Richard Blumenthal, D-Connecticut, suggested that President Trump's pick to fill the vacancy on the Supreme Court should recuse themselves from any potential court decisions that relate to the special prosecutor's ongoing investigation into the Trump campaign's possible ties to Russia.

"The president should not be permitted to appoint a justice who will decide whether or not he complies with a subpoena to testify before a grand jury or pardons himself," Blumenthal said on "Face the Nation" Sunday. "I believe that whoever is appointed ought to recuse himself and commit to recusing himself from those kinds of decisions that affect the personal finances or the special prosecutor investigation."

Special counsel Robert Mueller has sought an interview with Mr. Trump about his campaign's connections to Russian nationals and potential efforts to obstruct justice while in office. Rudy Giuliani, the president's attorney, has said that he would fight any attempt by Mueller to issue a grand jury subpoena and compel Mr. Trump's testimony, which could set up a legal challenge that potentially makes its way to the Supreme Court.

Blumenthal also said that an upcoming meeting between Mr. Trump and Russian President Vladimir Putin in Helsinki on July 16 is "deeply alarming."

Blumenthal's comments come after Supreme Court Associate Justice Anthony Kennedy announced last week that he would be retiring on July 31, giving Mr. Trump his second Supreme Court pick. Mr. Trump said he plans to announce Kennedy's successor on July 9 and will be picking from a list of 25 names last circulated when nominating Supreme Court Justice Neil Gorsuch to the bench last year.

Kennedy's vacancy, however, has many Democrats worried that the court will be decidedly conservative for decades. Blumenthal said that he's "never seen a court that is so polarized and so politicized," and that Mr. Trump's next decision to fill the bench "will shape the court for years to come."

"It could lead to criminalizing reproductive rights, as they were prior to Roe v. Wade," Blumenthal said. "Women were prosecuted and women died and women were denied access to contraception and the morning-after pill, and the same with the health insurance protections. These are real lives, real impacts."