(CNN) The top Democrats in Congress on Friday called for President Donald Trump to cancel his upcoming summit with Russian President Vladimir Putin after the Justice Department announced indictments against 12 Russian nationals, that accused them of engaging in a "sustained effort" to hack Democrats' emails and computer networks.

"President Trump should cancel his meeting with Vladimir Putin until Russia takes demonstrable and transparent steps to prove that they won't interfere in future elections. Glad-handing with Vladimir Putin on the heels of these indictments would be an insult to our democracy," Senate Minority Leader Chuck Schumer said in a statement.

The top Democrat in the House, Rep. Nancy Pelosi of California, tweeted, "@realDonaldTrump must immediately cancel his meeting with Putin."

Pelosi had said in an earlier statement, "The stakes for the upcoming Trump-Putin meeting could not be higher. President Trump must demand and secure a real, concrete and comprehensive agreement that the Russians will cease their ongoing attacks on our democracy. Failure to stand up to Putin would constitute a profound betrayal of the Constitution and our democracy."

The call to cancel the summit came after a week in which Democrats have expressed widespread concerns about Trump's ability to sit down and challenge Putin in a one-on-one meeting, which is scheduled for Monday. White House press secretary Sarah Sanders said Friday the summit will not be canceled.

In an interview on Capitol Hill, Virginia Sen. Mark Warner, the top Democrat on the Senate Intelligence Committee, said he is concerned that the President's "ad-hoc" style of going into meetings and "winging it" is not appropriate and that the meeting should be called off with Putin.

Warner said he's concerned the US "President can be taken advantage of" by Putin, and that if a meeting cannot have additional attendees it should be scrapped.

"There should be no one-on-one meeting between this President and Mr. Putin," Warner told reporters Friday.

Sen. Tammy Duckworth, an Illinois Democrat, also called for scrapping the meeting.

"We must bring to bear the full force of U.S. sanctions against Russia as well as consider their expansion against broader sectors of the Russian economy," Duckworth said in her statement. "Donald Trump must immediately cancel his planned summit with Vladimir Putin until Russia demonstrates its willingness to come back into the community of nations that respect the rule of law, legal norms and democratic institutions."

The Justice Department announced its indictments in special counsel Robert Mueller's investigation of Russian interference in the 2016 election. All 12 defendants are members of the GRU, a Russian federation intelligence agency within the main intelligence directorate of the Russian military, who were acting in "their official capacities."

Rep. Jerry Nadler, the top Democrat on the House Judiciary Committee, said Trump should demand the extradition of the Russians indicted on Friday, but he predicted that would not happen.

"He should demand that," said Nadler of New York. "I'm sure he won't."

Nadler said he didn't think that Trump should cancel the summit, but he agreed that the President should not be meeting with Putin alone.

Sen. Bob Menendez, the top Democrat on the Senate Foreign Relations Committee, also called for "the Russian spies indicted by the United States for interfering in the 2016 U.S. presidential election."

"Second, the Treasury Department must immediately impose sanctions mandated by Congress on the Russian intelligence officers indicted today," said Menendez of New Jersey. "And third, the President should demand Putin return Crimea to Ukraine, release individuals from Crimea imprisoned by Russia on political grounds, and fulfill his pledge to remove Iran from Syria."

"It is time for this President to stand up for America. It's time for him to put on his big boy pants and push back against Russia," California Rep. John Garamendi said in an interview with CNN's Wolf Blitzer on "The Situation Room."

"If we continue to be a little baby in the background as the President thinks we should be, then we're going to continue to get pushed around and there's going to be a very serious consequence in Europe, in the United States, in every free election around this world," said the member of the House Armed Services committee.

This story has been updated and will continue to update with additional developments.