Senate Minority Leader Charles Schumer Charles (Chuck) Ellis SchumerBrady gun control group gets rebranding Brennan fires back at 'selfish' Trump over Harry Reid criticism Trump rips Harry Reid for 'failed career' after ex-Dem leader slams him in interview 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 Warner Mark Robert WarnerVirginia man charged after threatening Sen. Mark Warner Cohen grilled by Senate Intelligence panel Hillicon Valley: Senators urge Trump to bar Huawei products from electric grid | Ex-security officials condemn Trump emergency declaration | New malicious cyber tool found | Facebook faces questions on treatment of moderators 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 Feinstein Dianne Emiel FeinsteinSenate confirms Trump court pick despite missing two 'blue slips' Hillicon Valley: Senators urge Trump to bar Huawei products from electric grid | Ex-security officials condemn Trump emergency declaration | New malicious cyber tool found | Facebook faces questions on treatment of moderators Ocasio-Cortez adviser says Sunrise confrontation with 'old-timer' Feinstein 'sad' 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 Cummings Elijah Eugene CummingsFive things to watch as Michael Cohen testifies The Memo: Capitol Hill braces for Cohen fireworks Overnight Health Care: Senators grill drug execs over high prices | Progressive Dems unveil Medicare for all bill | House Dems to subpoena Trump officials over family separations 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.