Senate Minority Leader Charles SchumerCharles (Chuck) Ellis SchumerSenate confirms Trump judicial nominee criticized for being hostile to LGBT community Senate confirms Trump judicial nominee criticized for being hostile to LGBT community Democrats detail new strategy to pressure McConnell on election security bills MORE (D-N.Y.) is warning President Trump not to interfere with special counsel Robert Mueller's Russia investigation after Paul Manafort, Trump's former campaign chairman, was charged as part of the probe. 

“The President must not, under any circumstances, interfere with the special counsel’s work in any way. If he does so, Congress must respond swiftly, unequivocally, and in a bipartisan way to ensure that the investigation continues," Schumer said in a statement. 

He added that "the rule of law is paramount in America and the investigation must be allowed to proceed unimpeded."

Manafort has been charged with 12 counts including conspiracy against the United States, according to the special counsel's office. Manafort’s former business partner and protegé, Rick Gates, who was ousted from the pro-Trump group America First Policies in April, has also been charged.

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The charges are related to work done by Manafort and Gates on behalf of a pro-Russia political party in Ukraine. 

Trump has previously flirted with firing Mueller, sparking bipartisan backlash on Capitol Hill. 

Two groups of senators have introduced legislation that would limit Trump's ability to fire Mueller, or have the Justice Department fire him, without a court's approval. And Democrats have warned Trump against trying to pardon individuals caught up in the investigation. 

Sen. Mark WarnerMark Robert WarnerFacebook's new cryptocurrency raises red flags for critics Facebook's new cryptocurrency raises red flags for critics Hillicon Valley: Senate sets hearing on Facebook's cryptocurrency plans | FTC reportedly investigating YouTube over children's privacy | GOP senator riles tech with bill targeting liability shield | FAA pushed to approve drone deliveries MORE (D-Va.), the top Democrat on the Intelligence Committee, said it is "imperative" after Monday's charges and with the investigation still ongoing that Congress move to protect the "independence of the special counsel."

"Members of Congress ... must also make clear to the president that issuing pardons to any of his associates or to himself would be unacceptable, and result in immediate, bipartisan action by Congress," Warner added.

Sen. Dianne FeinsteinDianne Emiel FeinsteinDemocrats detail new strategy to pressure McConnell on election security bills Democrats detail new strategy to pressure McConnell on election security bills Hillicon Valley: GOP senator wants one agency to run tech probes | Huawei expects to lose B in sales from US ban | Self-driving car bill faces tough road ahead | Elon Musk tweets that he 'deleted' his Twitter account MORE (D-Calif.), the top Democrat on the Judiciary Committee, said on Monday that she would "continue to support Bob Mueller as he follows the facts — his independence must remain sacrosanct." 

“I’m also more convinced than ever that both the Judiciary Committee and Intelligence Committee must continue their oversight investigations. Congress must get to the bottom of possible obstruction of justice and collusion as well as Russia’s interference with our democratic institutions," Feinstein added. 

In addition to Mueller's investigation, several congressional panels, including the Senate Judiciary and Intelligence committees, are investigating Russia's election interference. 

But House Minority Leader Nancy Pelosi (D-Calif.) is doubling down on her months-long push to create an independent, bipartisan panel to lead an investigation into the 2016 election and any potential collusion between Moscow and the Trump campaign. 

“Even with an accelerating Special Counsel investigation inside the Justice Department, and investigations inside the Republican Congress, we still need an outside, fully independent investigation to expose Russia’s meddling in our election and the involvement of Trump officials,” she said in a short statement. 

House Democrats are pushing legislation, sponsored by Reps. Elijah CummingsElijah Eugene CummingsCummings requests interview with Census official over new allegations on citizenship question Cummings requests interview with Census official over new allegations on citizenship question Top Democrats question legal basis for appointing Cuccinelli as temporary immigration chief MORE (D-Md.) and Eric Swalwell (D-Calif.), that would create a panel consisting of a bipartisan group of outside experts and full-time staff to look into Russia's election interference.

Trump, as well as GOP leadership in both chambers, have been cool to the idea, however, arguing that the ongoing investigations in both chambers are sufficient. 

--Mike Lillis contributed to this report, which was updated at 11:31 a.m.