In a letter addressed to Attorney General Jeff Sessions and Deputy Attorney General Rod Rosenstein, the Republicans said they were writing to "request assistance in restoring public confidence in our nation's justice system and its investigators, specifically the Department of Justice (DOJ) and the Federal Bureau of Investigation (FBI)."
The lawmakers said they presumed investigation of potential Russian influence on the U.S. presidential election was covered by special counsel Robert Mueller, but that they "are not confident that other matters related to the 2016 election and aftermath are similarly under investigation" by the former FBI director.
"The unbalanced, uncertain, and seemingly unlimited focus of the special counsel's investigation has led many of our constituents to see a dual standard of justice that benefits only the powerful and politically well-connected," the letter said. "For this reason, we call on you to appoint a second special counsel to investigate a plethora of matters connected to the 2016 election and its aftermath, including actions taken by previously public figures like Attorney General Loretta Lynch, FBI Director James Comey, and former Secretary of State Hillary Clinton."
Last year, the Justice Department declined to charge Clinton or her associates for Clinton's handling of classified information while at the State Department. As a candidate, Trump threatened to appoint a special prosecutor to look into Clinton's actions.
Comey had made a public announcement about the FBI's recommendation that the Justice Department not pursue charges against Clinton. He had said "no reasonable prosecutor" would bring a case against the former secretary of state for her handling of government emails. That conclusion was widely panned by Republicans.
Mueller, meanwhile, was appointed in May following Trump's dismissal of Comey and after the former FBI director's accounts about private conversations with the president started to surface.
Although the Thursday letter will surely be deemed a cynically partisan move by those on the left, the lawmakers attempted to address those criticisms.
"Our call for a special counsel is not made lightly. We have no interest in engendering more bad feelings and less confidence in the process or governmental institutions by the American people. Rather, our call is made on their behalf. It is meant to determine whether the criminal prosecution of any individual is warranted based on the solemn obligation to follow the facts wherever they lead and applying the law to those facts."
Still, Thursday's letter aligns with recent messages from the White House.
Trump has repeatedly lashed out and tried to shift the focus to Clinton amid his frustration with federal and congressional investigations into whether his campaign coordinated with Moscow. He has called the probe, led by Mueller, a politically charged "witch hunt."
The man Trump has picked to lead the FBI, Christopher Wray, has disputed that assertion.
Trump also recently lashed out at Rep. Adam Schiff of California, the top Democrat on the House Intelligence Committee, which is investigating Moscow's role. He called Schiff "sleazy" and "totally biased" and accused him of using Russia as an excuse for Democrats' performance in the election.
—CNBC's Jacob Pramuk contributed to this report.