Watch CNN's interview with Sen. Dianne Feinstein about the federal investigations into Russian interference in the US election on "State of the Union" this Sunday, June 11, at 9 a.m. and noon ET.
"It is my strong recommendation that the Judiciary Committee investigate all issues that raise a question of obstruction of justice," the California Democrat wrote in a letter to Senate Judiciary Chairman Chuck Grassley
on Friday. "These issues should be developed by our legal staff, presented to us, and be subject to full committee hearings."
Feinstein is the top Democrat on the Judiciary panel and a member of the intelligence committee, both of which are investigating Russia's efforts to influence the 2016 presidential election and related questions over the Trump campaign's contacts with Russian officials. Department of Justice special counsel Robert Mueller is also leading an investigation into those issues.
In the letter, Feinstein told Grassley she is "concerned" about Director of National Intelligence Dan Coats' and National Security Agency Director Admiral Rogers' refusals to answer questions from senators, adding that she wants to determine whether Trump asked Coats or Rogers "to take any action" on the Russia investigation.
"As I have mentioned to you directly, I am supportive of issuing subpoenas in those cases where we do not receive cooperation," she wrote.
Judiciary Committee spokesman Taylor Foy said Grassley "appreciates Ranking Member Feinstein's support and experience" in the committee's oversight activities.
"The two have worked closely on the committee's review of matters related to Russian interference and the circumstances of James Comey's removal, including jointly seeking any White House tapes and the Comey memos," he said. "Grassley values her input and welcomes the opportunity work together to gather the facts on behalf of the American people."
Feinstein's letter came a day after former FBI Director James Comey testified before the intelligence committee about his conversations with Trump.
Comey, who was fired while leading the probe into Russia's interference in the election, said Trump asked him to drop an investigation into former national security adviser Michael Flynn and implied Trump may have become the subject of investigation himself for interfering in the FBI's work. He repeatedly called the President a liar.
"You (Grassley) and I agree that these matters -- termination of the FBI Director and any efforts to interfere with the independence of ongoing investigations -- fall squarely in the jurisdiction of the Judiciary Committee," Feinstein wrote in the letter.
Feinstein said she also believes the committee should hear from officials Comey said he spoke with about his interactions with Trump, including Attorney General Jeff Sessions, Deputy Attorney General Rod Rosenstein and then-Deputy FBI Director Andrew McCabe, who is now the acting director of the bureau.
Democratic Sen. Patrick Leahy, who is also a member of the Judiciary Committee, backed Feinstein's request on Twitter.
"I couldn't agree more with @SenFeinstein," he tweeted Friday. "The American people deserve answers."