Senate Democrats pressed a top Justice Department nominee Tuesday to promise the appointment of a special prosecutor to oversee the ongoing federal inquiry into Russia's intervention in the U.S. election.

If confirmed as deputy attorney general, Maryland U.S. Attorney Rod Rosenstein would assume management of the investigation following last week's decision by Attorney General Jeff Sessions to recuse himself. Sessions' abrupt disqualification came after reports of meetings with the Russian ambassador to the United States that he twice failed to disclose to the Senate Judiciary Committee during his January confirmation hearing.

California Sen. Dianne Feinstein, the ranking Democrat on the Judiciary panel, said recent disclosures about contacts between Russian authorities and Trump associates require the appointment of a "respected prosecutor'' because recent disclosures about communications between Trump associates and Russian officials demonstrate the "perception'' of a conflict of interest.

"I do not say this because I question the integrity of Mr. Rosenstein, I do not,'' Feinstein said. "This is about something bigger than one individual.''

Judiciary Chairman Chuck Grassley, R-Iowa, said such requests for a special counsel were "premature at best.''

"Special counsel inquiries under the current department regulations are not the best way to ensure transparency and accountability,'' Grassley said. "There is no mandatory public report or other finding at the end of the investigation if no charges are filed. The investigations can just disappear without the public ever understanding what the facts were. So, the notion that somehow a special counsel will bring facts to light just isn’t true.”

Rosenstein's nomination to the second-highest ranking post at the Justice Department has drawn intense scrutiny as an increasing number of top aides to President Trump have acknowledged meeting with Russian envoy Sergey Kislyak in the months prior to Trump's election and inauguration. The ongoing FBI investigation is reviewing communications between Trump associates and Russian government officials.

On Monday, Sessions asserted that his January confirmation testimony to the Senate Judiciary Committee was "correct,'' saying that he did not disclose meetings with the Russian ambassador to the United States because he was not specifically asked about them.

Sessions said he always believed that he had answered the committee's questions "honestly'' about Trump surrogates' contacts with Russian officials.

"I did not mention communications I had had with the Russian ambassador over the years because the question did not ask about them,'' Sessions said in a letter to the committee, explaining the disputed testimony.

Sessions referred to a question posed by Sen. Al Franken, D-Minn., who asked Sessions what he would do if he became aware that "anyone affiliated with the Trump campaign communicated with the Russian government in the course of this campaign.''

"I'm not aware of any of those activities,'' Sessions responded at the time. "I have been called a surrogate at a time or two in that campaign and I didn't have, have — did not have communications with the Russians.''

Democrats seized on Sessions' response, and a similar answer provided to Sen. Patrick Leahy, D-Vt., in a written response, as at least misleading and disqualifying him from managing the FBI's continuing Russia investigation. Others, including Senate Minority Leader Chuck Schumer of New York and House Minority Leader Nancy Pelosi of California, have called for the former Alabama senator to resign.

"I answered the question, which asked about a 'continuing exchange of information during the campaign between Trump's surrogates and intermediaries for the Russian government,' honestly,'' Sessions maintained.