Obama and Republican leader pledge to work together
The US Senate's new Republican leader and President Barack Obama have both promised to end the political gridlock that has so frustrated American voters.
Republicans made historic gains in the mid-term elections and now control both legislative chambers.
Incoming Senate leader Mitch McConnell said he would make the ineffective Senate function and pass bills.
Mr Obama said he was "eager to work with the new Congress to make the next two years as productive as possible".
The election campaign was characterised by widespread frustration expressed by voters about the inability of Congress to work together.
To the Americans who voted for change, the president said: "I hear you."
He told a White House news conference that both parties must address those concerns, but he admitted that as president he had a "unique responsibility to try to make this town work".
On Friday, he will host a meeting at the White House with Democratic and Republican leaders.
"We can surely find ways to work together," Mr Obama said. "It's time for us to take care of business."
But he warned he would act on his own to reduce deportations and improve border security - action he had delayed until after the election, to the fury of some Latino voters.
Earlier on Wednesday, Mr McConnell pledged to make the Senate more productive.
"The Senate in the last few years basically doesn't do anything," he said. "We're going to go back to work and actually pass legislation."
He also vowed to "work together" with Mr Obama on issues where they can agree, such as trade agreements and tax reform.
Working within a two-party political system did not mean "we have to live in perpetual conflict", he added.
Also on Wednesday, the chairman of the Republican National Committee called resounding Republican mid-term victories a "direct rejection of the Obama agenda".
"[Americans] want nothing to do with the policies of Barack Obama," Reince Priebus told reporters.
Analysis, Jon Sopel, BBC North America editor
Barack Obama's unpopularity in the run-up to these mid-term elections is hard to exaggerate. One of the things that is lost in the big picture of the night is some of the sidebar poll findings - the American people are fed up with all their politicians. It's not just the occupant of the White House, though as Harry Truman most famously noted, the buck stops with the president.
Mitch McConnell will be conscious of that, and will know that in two years' time, when it is not just the Senate but the presidency in play, the American people could be venting their spleen on him. Be fearful of the blame game.
That leaves the Kentucky senator with some important tactical decisions to make.
Throughout the campaign, Republicans focused on voter dissatisfaction with Mr Obama, a Democrat, describing the vote as a referendum on his presidency.
As the first results came in late on Tuesday, it became clear they had made the six gains they needed to win control of the Senate.
The Republicans won in Arkansas, Colorado, Iowa, Montana, North Carolina, South Dakota and West Virginia. The party now controls 52 seats, and is tipped to win at least one more as votes are counted in other states.
Republicans in numbers
100 Women elected to Congress - including Mia Love - first black Republican female
1st African American, Tim Scott, elected in the South since 1870
3rd George Bush - grandson and nephew of two former presidents
18 Age of Saira Blair, the youngest elected state legislator
30 Age of Elise Stefanik, youngest woman elected to US Congress
Their victory came on the back of a wave of discontent expressed by voters on the campaign trail - unhappy with an economic recovery they fail to feel the benefits of, and frustrated by political gridlock in Congress, which has already reached historic levels.
But echoing his successor's sentiment of unity, current Senate Majority Leader Harry Reid congratulated Mr McConnell in a short statement.
"The message from voters is clear - they want us to work together," said Mr Reid of Nevada, whose role in the soon-to-be Democratic minority remains uncertain.
"I look forward to working with Senator McConnell to get things done for the middle class."
The Republicans are also projected to increase their majority - by at least 10 seats - in the House of Representatives to levels not seen since before World War Two.
They also made gains among the 36 governorships up for re-election.
The Republicans will now have the power to complicate, if not block completely, Mr Obama's agenda in the last two years of his tenure in the White House.
Control of the Senate will also enable the Republicans to stymie his ability to name new federal judges, cabinet members and senior government officials.
In the governor's races, Republican incumbents survived some tough re-election battles and scored some surprising victories, cementing their success across several levels of government.
Voters approved ballot measures legalising cannabis in Oregon and Washington DC.
And three states - South Dakota, Arkansas and Nebraska - approved increases in the minimum wage.