Pressure is growing on Republican leaders to support a special prosecutor to investigate contacts between Donald Trump's presidential campaign, transition team and Russian intelligence agents.

Some Republican lawmakers say a special prosecutor may be warranted, depending on what facts emerge regarding ties between the Trump campaign and the Russian government.

They say evidence indicating that Trump advisers broke the law may necessitate special counsel — but so far nothing has reached that threshold.

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Sen. Lindsey Graham Lindsey Olin GrahamGOP senators say coronavirus deal dead until after election Tucker Carlson accuses Lindsey Graham of convincing Trump to talk to Woodward Trump courts Florida voters with moratorium on offshore drilling MORE (R-S.C.), a member of the Judiciary Committee, floated the possibility of a special prosecutor at a CNN town hall on Wednesday night.

“There may be nothing there,” Graham said. “But if there is something there that the FBI believes is criminal in nature, then for sure you need a special prosecutor.”

Sen. Thom Tillis Thomas (Thom) Roland TillisDemocratic Senate candidate 'hesitant' to get COVID-19 vaccine if approved this year On Paycheck Protection Program, streamlined forgiveness is key Poll shows Biden and Trump neck and neck in North Carolina MORE (R-N.C.) said it might make sense to bring in a special prosecutor should more facts come to light.

“We’ll let the facts speak for themselves,” he said, adding that the Trump administration needs to be sensitive to appearances of conflict of interest.

“You just want to nip that because we don’t want this to be a distraction at the expense of so many things that need to be corrected at the Department of Justice,” Tillis said.

Democrats are turning up the heat, arguing that no one at the DOJ who answers to the president could be expected to act with complete impartiality.

“The Justice Department must immediately appoint a special prosecutor,” Senate Democratic Leader Charles Schumer Chuck SchumerOvernight Health Care: Schumer calls for Azar to resign over 'chaos' in coronavirus response CNBC's Cramer calls Pelosi 'crazy Nancy' in live interview Schumer calls for Azar to resign over 'chaos' in coronavirus response MORE (N.Y.) told reporters Thursday morning.

He said that person should be “beyond reproach, completely impartial, without any significant ties to either political party.”

Schumer noted that Justice Department guidelines call for a special prosecutor when a standard of investigation “would present a conflict of interest for the department or other extraordinary circumstances.”

“The most important thing we must do is ensure the integrity of the investigation,” he said.

“Has it already been compromised? What can we do to ensure it moves forward in a way that ultimately leads to the unvarnished truth?” he asked.

Other Democratic lawmakers, including Sens. Patrick Leahy Patrick Joseph LeahyBattle over timing complicates Democratic shutdown strategy Hillicon Valley: Russia 'amplifying' concerns around mail-in voting to undermine election | Facebook and Twitter take steps to limit Trump remarks on voting | Facebook to block political ads ahead of election Top Democrats press Trump to sanction Russian individuals over 2020 election interference efforts MORE (Vt.), Jack Reed John (Jack) Francis ReedWhen 'Buy American' and common sense collide Hillicon Valley: Russia 'amplifying' concerns around mail-in voting to undermine election | Facebook and Twitter take steps to limit Trump remarks on voting | Facebook to block political ads ahead of election Top Democrats press Trump to sanction Russian individuals over 2020 election interference efforts MORE (R.I.), Martin Heinrich Martin Trevor HeinrichSenate Democrats demand White House fire controversial head of public lands agency Senate Democrats seek removal of controversial public lands head after nomination withdrawal Five takeaways from final Senate Intel Russia report MORE (N.M.) and Gary Peters (D-Mich.), echoed the call for a special prosecutor.

Newly elected Democratic National Committee Chairman Tom Perez, a former Labor secretary during the Obama administration, said, “Trump’s Department of Justice has proven incapable of pursuing an independent investigation” into possibly improper ties between the administration and Russia.

Sessions held a press conference Thursday afternoon to announce that he would follow the recommendations of staff and recuse himself from any investigation into Russian ties to the administration.

Justice Department guidelines state that no employee may participate in a criminal investigation or prosecution if he or she has a personal or political relationship with the subject of the probe or prosecution.

Sessions was the first senator to endorse Trump and advised his campaign.

His statement of recusal came hours after several prominent Republicans on Capitol Hill urged him to step aside, following a Wednesday night Washington Post report that he had two meetings with Russian Ambassador Sergey Kislyak.

Sessions testified before the Senate Judiciary Committee in January that he “did not have communications with the Russians.” Those statements, which Sessions tried to explain at his press conference, prompted Democratic accusations that he misled Congress and may have perjured himself.

With Sessions on the sidelines, lawmakers are now turning to the tricky question of who should handle the investigation.

The recusal puts acting Deputy Attorney General Dana Boente, whom President Obama appointed twice to U.S. attorney jobs, in charge of the Justice Department — at least in the short term.

Democrats argued it would be unacceptable for Boente to oversee the investigation, arguing he is still in the “chain of command” at the Justice Department and could be subject to political influence from the White House.

“While Mr. Boente doesn't have the long political ties to President Trump Donald John TrumpTrump says he doesn't think he could've done more to stop virus spread Conservative activist Lauren Witzke wins GOP Senate primary in Delaware Trump defends claim coronavirus will disappear, citing 'herd mentality' MORE, he is still in the President’s chain of command and could be fired at will by the President, who has already fired the first person in this position,” Schumer said in a statement after Sessions recused himself.

“The DOJ regulations clearly require the appointment of a special prosecutor and the administration shouldn't ignore clear regulations a second time,” he added.

Trump’s deputy attorney general nominee, Rod Rosenstein, faces the Judiciary Committee next week and may ultimately make decisions about a DOJ probe once confirmed. Democrats have yet to discuss the possibility of Rosenstein taking over the probe.

If Boente declines to follow Democrats’ exhortations, they say they will pressure Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellGOP ramps up attacks on Democrats over talk of nixing filibuster MLB owner: It's 'very necessary' to vote for Trump Delta: Early departures saved flight attendants' jobs MORE (R-Ky.) and Speaker Paul Ryan Paul Davis RyanAt indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates Peterson faces fight of his career in deep-red Minnesota district MORE (R-Wis.) to support legislation that would empower a panel of judges to choose a special prosecutor.

Congress passed the Independent Counsel statute as part of the reforms enacted after the Watergate scandal that led to President Richard Nixon’s resignation.

The law required the attorney general to conduct preliminary investigations into allegations against high-level government officials and to refer the case to a three-judge court to appoint an independent counsel if deemed necessary.

It expired in 1999, after Democrats felt that independent counsel Ken Starr abused his power during his investigation into President Bill Clinton William (Bill) Jefferson ClintonTrump pulls into must-win Arizona trailing in polls Does Kamala Harris's music matter? President Nancy Pelosi? Don't underestimate what she might do in office MORE.

Schumer said if Boente doesn’t appoint a special counsel, Democrats will ask Republicans to pass a new version of the law with safeguards to prevent the kind of runaway investigation that many Democrats thought Starr was guilty of in the 1990s.

The issue is likely to surface Tuesday at the Judiciary Committee hearings on Rosenstein, the current U.S. attorney for Maryland.

The committee is also expected to consider Rachel Brand, Trump’s pick to serve as associate attorney general.

Both nominees require Senate confirmation, and Democrats could use that as leverage to push for the appointment of a special prosecutor.