WASHINGTON — Democrats on the Senate Judiciary Committee called on Tuesday for the appointment of a special counsel to lead the criminal investigation into Russian interference in the 2016 presidential election, saying the appointment was necessary to shield the inquiry from the appearance of political interference by the Trump administration.

“This is about more than just one individual,” said Senator Dianne Feinstein of California, the panel’s ranking Democrat. “This is about the integrity of the process and the public’s faith in our institution of justice.”

But the Republican chairman of the panel, Senator Charles E. Grassley of Iowa, said he saw no need for the appointment of a special counsel as the panel took up the confirmation of Mr. Trump’s nominee to be deputy attorney general, Rod J. Rosenstein.

“There are times when special counsels are appropriate,” Mr. Grassley said. “But it’s far too soon to tell here. And even if there were evidence of a crime related to any of these matters, once confirmed, Mr. Rosenstein can decide how to handle it. I know of no reason to question his judgment, integrity or impartiality.”