Both parties hailed the results of Tuesday's midterm elections as a victory, with Democrats signalling they would use their newly gained control of the House as a check on the Trump administration.
Republicans, too, claimed the results a win, casting their increased Senate majority as a huge success and warning Democrats against impeaching the President.
United States President Donald Trump declared the night a "tremendous success" on Twitter. He called Senate majority leader Mitch McConnell to congratulate him on the "historic Senate gains", press secretary Sarah Sanders told reporters at the White House.
House minority leader Nancy Pelosi, who may become the House Speaker when the new Congress convenes in January, said: "Tomorrow will be a new day in America... Today is more than about Democrats and Republicans. It's about restoring the Constitution's checks and balances to the Trump administration."
She added that the Democrat agenda would include stopping the Republican party's "assault" on healthcare policies.
Other Democrat leaders adopted a similar line, with Democratic National Committee chairman Tom Perez calling their taking control of the House for the first time since 2010 a win for democracy.
"Now it's time to get to work restoring sanity to our government, holding Trump accountable and working to build a better future for our country," he posted on Twitter.
Democrat congressman Adam Schiff, who is likely to become the next chair of the House Intelligence Committee, told MSNBC that Congress would once again undertake its role of conducting oversight of the Trump administration and that it would do so responsibly.
He accused Republicans of abdicating this responsibility and talked about seeing through and protecting the Russia investigation by special counsel Robert Mueller.
He said: "I think the chances that Bob Mueller will be able to finish his work improved."
Ms Pelosi sought to assuage fears of a government gridlock and called for bipartisanship. In her victory speech, she said Democrats had a "responsibility to find our common ground when we can, stand our ground where we can".
In a PBS NewsHour interview, she said she was not in favour of impeaching the President, which Democrats can do now that they control the House. "It depends on what happens in the Mueller investigation. But that is not unifying. If that happens, it would have to be bipartisan and the evidence would have to be so conclusive."
Ms Sanders, in an interview with Fox News, similarly said the House should focus more on legislation than investigation. "I believe that's what should happen. I think that's what America wants to see. If Democrats take the House, they shouldn't waste time investigating. They should focus on doing what the people have put them there to do."
She noted Mr Trump's role in hitting the campaign trail for candidates, saying: "The candidates who embraced the President and whom the President has gone in to campaign for over the past several weeks are doing very well tonight."
South Carolina senator Lindsey Graham said in a separate Fox News interview that Mr Trump "has a lot to be proud of in terms of creating the enthusiasm" in red states like Indiana, which voted out incumbent Democrat senators, widening the GOP's majority.
"Without him, I don't think we would have had the night we had," he said, adding that the Republican Senate would continue to confirm conservative judges.
Outgoing House Speaker Paul Ryan, who did not run for re-election, called for bipartisanship. "We don't need an election to know we are a divided nation and now, we have a divided Washington. As a country and a government, we must find a way to come together to find common ground and build on the successes of this Congress."
