The two senators want the transcript of the committee's interview with Glenn Simpson, a founder of Fusion GPS, released.
Fusion initially was hired through a conservative website, the Washington Free Beacon, during the Republican primaries to dig up dirt on Trump.
Feinstein released the testimony after the panel's Republican chairman, Charles Grassley, on Friday called for a criminal investigation into former British spy Christopher Steele, who was working for Fusion GPS when he compiled a "dossier" of allegations of financial and personal links between Trump, his advisers and Russian Federation.
Republicans and Democrats have tangled in recent weeks over the origins of the dossier, which was funded in part by Trump's political opponents, and how the FBI and other agencies may have used the dossier in their investigations.
"The innuendo and misinformation circulating about the transcript are part of a deeply troubling effort to undermine the investigation into potential collusion and obstruction of justice", said Dianne Feinstein, who is the senior Democrat on the Senate Judiciary Committee.
In an angry statement, Grassley said that "neither the special counsel, nor any other congressional committee, has released transcripts of private interviews in the course of their investigations".
Senate judiciary committee chairman Chuck Grassley and Lindsey Graham said they had passed a classified memorandum to the DoJ relating to communications between Mr Steele and "multiple U.S. news outlets".
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The resulting memos, written over the summer and fall of 2016, were explosive: They alleged that the Russian government had compromising material on the president and that Trump's campaign colluded with Russia to defeat Clinton during the presidential elections.
"The only way to set the record straight is to make the transcript public", she said.
In his testimony, Simpson addressed the point that the information Steele reported might not be factually correct.
One reason, according to Simpson, was a story in The New York Times on October 31, 2016 that said the Federal Bureau of Investigation hadn't found any connections between Trump world and the Russian attack on the election. On Jan. 2, Simpson and fellow Fusion GPS co-founder Peter Fritsch called on congressional investigators to release their testimony.
Fusion GPS was hired in mid-2016 by a lawyer for Hillary Clinton's presidential campaign and the Democratic National Committee to dig into Trump's background. Chuck Grassley, issued a criminal referral last week for Steele, alleging the committee had reason to believe that the former spy had lied to authorities about his conversations with the press regarding the dossier.
When asked who that source may have been an answer was declined on the basis of "security", with Mr Simpson adding that "people who get in the way of the Russians tend to get hurt".