Robert Mueller
Special Counsel Robert Mueller departs after briefing the House Intelligence Committee on Capitol Hill in Washington, June 20, 2017. Reuters

Special counsel Robert Mueller met with members of the House Intelligence Committee on Tuesday to discuss how to co-exist while parallelly investigating the potential connections between Russian officials and the 2016 presidential campaign of President Donald Trump.

The special counsel met with Rep. Adam Schiff (D-California) and Rep. Mike Conaway (R-Texas), who took over as the top Republican for the panel's Russia investigation earlier this year.

"We had a productive meeting with Special Counsel Mueller this afternoon to deconflict our concurrent investigations, and look forward to continuing our dialogue with him as both investigations progress," Conaway and Schiff said in a joint statement.

Mueller however declined to comment as he left the meeting Tuesday, CNN reported.

Read: Did Jared Kushner’s Middle East Role Get Affected By Robert Mueller’s Investigation Into His Business Deals?

This meeting between Mueller and the House leaders came a week after he held a similar meeting with Senate Intelligence Committee Chairman, Richard Burr and its ranking Democrat Sen. Mark Warner. The committee is conducting a third investigation into possible interference into the election that saw testimonies in recent weeks from former FBI Director James Comey and Deputy Attorney General Rod Rosenstein, among others, according to reports.

The special counsel, who can be appointed by either the Attorney General or by Congress, was appointed by Deputy Attorney General Rod Rosenstein in in May after the Attorney General Jeff Sessions recused himself from matters related to the Russia probe.

However, the special counsel's independent probe will not affect the House Intelligence Committee's investigation. As Schiff said: "The appointment of a special counsel is not a substitute for a vigorous investigation in Congress and the House Intelligence Committee will take steps to make sure our investigations do not conflict and ensure the success of both efforts." He added: “We will also want to make certain that the special counsel has all the resources it needs to undertake this important task.”

According to Justice Department regulations, "the special counsel shall not be subject to the day-to-day supervision of any official of the department.” However, the attorney general (or in this case Rosenstein ) can block major investigative steps if they determine that the action “is so inappropriate or unwarranted under established departmental practices that it should not be pursued." If that happens, Rosenstein must explain his decision to the Congress.

After Mueller's appointment last month, Congress reacted in a positive manner. Maine Democratic Rep. Chellie Pingree tweeted an independent commission was necessary to have "full confidence" in the FBI's probe. South Carolina Republican Rep. Jeff Duncan meanwhile called Mueller a "great choice."

Read: Donald Trump May Fire Robert Mueller Citing Conflict Of Interest

"The decision by the deputy attorney general to appoint former FBI Director Robert Mueller as a special counsel confirms that the investigation into Russian intervention into our election will continue, as stated last week by Acting FBI Director Andrew McCabe," Senate Majority Leader Mitch McConnell had said in a statement, as reported by CBS News. He added: "The Senate Select Committee on Intelligence will also continue its investigation into this matter."