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(CNN) —  

Senate Democrats emerged from a classified election security briefing Wednesday complaining the Trump administration is still not doing enough to thwart foreign actors like Russia from interfering in the 2020 US elections and Senate Republicans are not doing enough to beef up election security laws.

“Interference in our elections is a very, very serious problem and it is obvious we have to do a lot more at both the public sector and private sector levels to combat it,” said Senate Minority Leader Chuck Schumer, a New York Democrat, after the all-senators briefing. “I am very worried about what the Russians and others might do in 2020.”

Democratic Sen. Chris Murphy of Connecticut said he believes President Donald Trump is reluctant to firmly hold Russia and President Vladimir Putin accountable for interference in 2016.

“We have a president who is actively undermining election security efforts and a lot of people working at the top of these agencies who are trying to do the right thing,” Murphy said.

The briefing was led by Director of National Intelligence Dan Coats, FBI Director Chris Wray, acting Homeland Security Secretary Kevin McAleenan and other officials. They briefed the full House before meeting with the senators.

Mississippi Democratic Rep. Bennie Thompson, the chairman of the House Homeland Security Committee, emerged from the meeting saying the briefers assured members they have the “resources” to secure election systems – but Democrats still have more questions.

“There’s real interest on the part of members of Congress to know who’s in charge, what are the operating procedures for the process to move forward – and the answers were not as clear as they needed to be,” Thompson told reporters.

Democrats and Republicans have battled over the best way to respond to Russian interference in the 2016 elections. Democrats want a more robust approach pushed by the federal government, while Republicans argue improvements to the election system were made in the last Congress – which limited problems in the 2018 campaign – and that further reforms, if needed, should be made by states.

Those differences were on display before the briefing with Senate Majority Leader Mitch McConnell argued in a floor speech that even before the briefing occurred, Democrats had decided that a “brand-new, sweeping Washington, DC, intervention is just what the doctor ordered.”

Schumer pushed back, saying that it was McConnell who was “misguided” to declare before the briefing took place that Washington didn’t have a larger role to play securing elections and fighting interference.

“I hope today’s briefing provides members with specific information about what the departments and agencies are doing to combat the threat to our elections and what we ought to do next,” Schumer said. “After it concludes, we cannot let this issue sit on the backburner. Democrats and Republicans alike must roll up their sleeves and get to work, the Majority Leader included.”

Sen. Marco Rubio, a Florida Republican who has authored bipartisan legislation to impose new sanctions on those who try to interfere in US elections, said he believes the administration is prepared for 2020.

“We spent a lot of time on the tactics used. Whether it’s messing with the elections’ systems or influence operations. It’s all psychological warfare aimed at undermining us from the inside out. Drive societal divisions, undermine confidence in our elections and our democracy,” he said. “In my view, they are doing everything they can to be ready for 2020.”

South Carolina Republican Sen. Lindsey Graham agreed: “I was very impressed. They all said the President has given them every authority they have asked for. No interference from the White House. They are building on the success of 2018.”

Sen. Roy Blunt, a Missouri Republican who chairs the Senate Rules Committee that has oversight of elections, said he didn’t expect new legislation to emerge from this process. He said a lot of progress has already been made and Republicans who control the chamber would rather leave it to the states and localities.

“I think the federal government can partner, I think the federal government can encourage. Most of those states have money available to them form the $382 million that was made available two years ago. But I would not be of the idea that it’s the federal government’s job to come in and take over other states and local responsibility,” Blunt said.

Alabama Rep. Mike Rogers, the top Republican on the House Homeland Security Committee, said after the briefing that no new legislation on the subject would be necessary.

“I wouldn’t say we’ve got the need for election security legislation,” he said. “The question was asked and they basically said they’ve got the authority they need right now.”

CNN’s Ashley Killough and Morgan Rimmer contributed to this report.