The FBI is also conducting a parallel probe, which reportedly includes special counsel Robert Mueller looking into whether the president obstructed justice. He wrote in multiple social media posts that he views Mueller - a long-serving former Federal Bureau of Investigation director respected by both parties - as leading a biased probe with the singular aim of dislodging Trump.
"The message the president is sending through his tweets is that he believes the rule of law doesn't apply to him and that anyone who thinks otherwise will be fired", Feinstein said.
In a series of statements on Twitter Thursday, Trump repeated his assertion that Mueller's investigation into Russian interference in the 2016 campaign is a "WITCH HUNT" based on the "phony" premise of possible collusion between Russia and a cadre of Trump campaign associates.
Deputy Attorney General Rod Rosenstein, who appointed Mueller last month, testified Tuesday he has seen no evidence of good cause to fire Mueller.
He tweeted, "After 7 months of investigations & committee hearings about my "collusion with the Russians", nobody has been able to show any proof".
"You are witnessing the single greatest WITCH HUNT in American political history - led by some very bad and conflicted people!" Joe Lieberman, former Oklahoma Governor Frank Keating, former FBI official Richard McFeely and acting FBI Director Andrew McCabe, met with Trump at the White House.
The department would not comment on the record on whether Trump, who has repeatedly complained about leaks on the case, requested the statement.
"Why is that Hillary Clintons family and Dems dealings with Russian Federation are not looked at, but my non-dealings are?", Trump tweeted just before 4 p.m. EDT.
The meeting comes a day after lawmakers questioned Justice Department officials about the probe and Mueller's independence, and after a friend of President Donald Trump said the White House was considering firing Mueller.
Mr Trump's tweet sparked the derision of social media users.
"Why is that Hillary Clintons family and Dems dealings with Russian Federation are not looked at, but my non-dealings are?" he asked at one point.
Trump has told associates he has the legal authority to fire Mueller.
When she was asked to discuss the president's tweet, the deputy press secretary reportedly said that she couldn't because "I'm not the president". Trump tweeted Thursday afternoon.