Republicans have taken control of the US Senate and are fighting to keep their majority in the House of Representatives, which would produce a full sweep of power in Congress alongside Donald Trump in the White House.

A unified Republican grip on Washington would set the course for Mr Trump’s agenda or if Democrats wrest control of the House, it would provide an almost certain backstop, with veto power over the White House.

Speaking early on Wednesday at his election night party in Florida, Mr Trump said the results delivered an “unprecedented and powerful mandate” for Republicans.

(PA Graphics)

He called the Senate victory “incredible” and he praised House Speaker Mike Johnson, who dashed from his own party in Louisiana to join Mr Trump.

Vote counting in some races could go on for days, and control of the House is too early to call.

The rally for Republicans started early on election night in West Virginia, when Jim Justice, the state’s wealthy governor, flipped the seat held by retiring Senator Joe Manchin.

Republicans toppled Sherrod Brown in Ohio, the first incumbent senator to fall, with luxury car dealer and blockchain entrepreneur Bernie Moreno winning.

Democrat Sherrod Brown failed to win another term in Ohio (Jeff Dean/AP)

The unexpected battleground of Nebraska pushed Republicans over the winning line as incumbent Senator Deb Fischer brushed back a surprisingly strong challenge from independent newcomer Dan Osborn.

One of the most-watched Senate races, in Montana, was decided early on Wednesday.

Democrat Jon Tester, a popular three-term senator and “dirt farmer” in the fight of his political career lost to Trump-backed Tim Sheehy, a wealthy former Navy Seal, who made derogatory comments about Native Americans, a key constituency in the Western state.

All told, Senate Republicans have a chance to scoop up more seats, potentially delivering their most robust majority in years.

The fight for control of the House became a state-by-state slog, much of which unfolded far from the presidential race.

House races are focused in New York and California, where Democrats are trying to claw back some of the 10 or so seats where Republicans have made surprising gains in recent years.

Other House races are scattered around the country, with some of the most contentious in Maine, the “blue dot” around Omaha, Nebraska, and in Alaska.

To gain control of the House, Democrats need to flip four seats from Republicans, while holding all of their own, a tall task especially in congressional districts where Mr Trump has won.

It could come down to just a handful of seats, or as little as one, to determine House control.

Voters elected two black women to the Senate, Democrat Lisa Blunt Rochester of Delaware and Democrat Angela Alsobrooks, who defeated Republican Larry Hogan, the former governor, in Maryland.

Just three black women have served in the Senate, and never before have two served at the same time.

And in New Jersey, Andy Kim became the first Korean American elected to the Senate. The seat opened when Bob Menendez resigned this year after his federal conviction on bribery charges.

In the House, candidate Sarah McBride, a Democratic state lawmaker from Delaware who is close to the Biden family, became the first openly transgender person elected to Congress.

Sarah McBride has become the first openly transgender person elected to Congress (AP Photo/Pamela Smith)

What is still unclear is who will lead the new Republican Senate, as long-time leader Mitch McConnell prepares to step down from the post.

South Dakota Senator John Thune, the number two Republican, and Texas Senator John Cornyn, who previously held that post, are the front-runners to replace Mr McConnell in a secret-ballot election scheduled for when senators arrive in Washington next week.

Billions of dollars have been spent by the parties, and outside groups, on the narrow battleground for both the 435-member House and 100-member Senate.

If the two chambers do in fact flip party control, as is possible, it would be rare.

Records show that if Democrats take the House and Republicans take the Senate, it would be the first time that the chambers of Congress have both flipped to opposing political parties.