By Richard Cowan and Susan Cornwell

WASHINGTON (Reuters) - Republicans maintained their majorities in both chambers of the U.S. Congress in a momentous election on Tuesday in which Republican Donald Trump won the presidency, empowering the party to reshape Washington.

The Republican sweep sets up the United States for two years of "unified" government, which would normally mean significant policy change, although Trump's election was anything but normal and he will start his presidency with unusual handicaps.

Both Republican leaders on Capitol Hill held Trump at arm's length during the campaign. Trump offended and attacked some congressional Republicans on the stump, including House of Representatives Speaker Paul Ryan.

Early on Wednesday, shortly after Clinton conceded to Trump, Ryan said in a statement: "We are eager to work hand-in-hand with the new administration to advance an agenda to improve the lives of the American people."

Senate Majority Leader Mitch McConnell, also a Republican, said in a guarded and similarly timed statement: "The American people have chosen a new direction for our nation."

The new Congress will not convene until Jan. 3, but the "lame-duck" Congress will return next week and Republicans are set to begin the process of picking leaders for both chambers.

Ryan's position as speaker could be challenged by Republican conservatives who backed Trump and it remains to be seen if the president-elect himself will try to push Ryan out.

"Trump seems magnanimous right now," an aide to one of Trump's House supporters said after Trump stressed unity in his victory speech in New York. "We shall see."

In a huge disappointment to Democrats, Republicans were on a pace to lose only a handful of seats in the House, well below the double-digit losses some predicted.

Similarly, Democrats gained only one seat in the Senate, although a few races were still to be determined, including New Hampshire, where incumbent Republican Kelly Ayotte was deadlocked with Democrat Maggie Hassan early on Wednesday.

In Illinois, Democratic U.S. Representative Tammy Duckworth defeated Republican Senator Mark Kirk. Democrats needed to pick up a net five seats to win Senate control.

PREDICTIONS DEFIED

Republican successes came on the heels of big Republican gains in the 2014 congressional elections and defied predictions the party was in tatters and on the verge of splitting apart because of deep divisions over Trump.

Congressional Republicans are sure to flex their muscles on a range of legislation, not the least of which is fulfilling a six-year quest to repeal President Barack Obama's landmark healthcare law known as "Obamacare."

Republicans also campaigned on an agenda that shunned comprehensive immigration reform and opposed gun control and expanded environmental and financial regulations.

In the Senate, McConnell, a Kentucky Republican, was expected to remain at his post for at least the next two years.

Paul Sracic, who chairs the politics department at Youngstown State University in Ohio, said: “There was all this concern that Trump would damage Republicans down-ticket. Just the opposite happened" as Trump brought out more Republican voters.

Come January, Republicans will have to pivot from trying to block Obama's initiatives - such as his signature health insurance program Obamacare - to governing along with Trump.

"Republicans no longer have the luxury of being the opposition party, said Sarah Binder, a political science professor at George Washington University.

"For example, will they actually repeal Obamacare and agree what to implement in its place?" she added.

MCCONNELL'S PAYOFF

McConnell led conservatives' opposition to any Supreme Court nominee named by Obama following last February's death of conservative Justice Antonin Scalia. [nL1N1D42DX]

His gamble paid off and he will now await a nomination from Trump, likely dooming Obama's choice of federal judge Merrick Garland.

Star-power incumbent Republicans, such as Senator John McCain in Arizona and Marco Rubio in Florida, also scored victories.

Issues ranging from tax cuts to border security will now take center stage in Washington. Trump's opposition to trade deals with foreign countries puts in serious jeopardy the Trans-Pacific Partnership agreement negotiated by Obama that would cover economies from Japan to Chile.

"In terms of trade, I think TPP is dead. The stake went through its heart tonight,” Sracic said.

(Additional reporting by Ian Simpson; Editing by Kevin Drawbaugh and Peter Cooney)