Story highlights Former FBI Director James Comey gave his testimony on Thursday

Feinstein is a member of both the Judiciary and intelligence committees

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.

Washington (CNN) Sen. Dianne Feinstein is calling on the head of the Senate Judiciary Committee to investigate all issues related to obstruction of justice in the events leading up to the firing of FBI Director James Comey and the federal probe into Russian meddling in the 2016 election, using "subpoena authority if necessary."

"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.

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