WASHINGTON — Republicans seized control of the United States Senate on Tuesday, riding a wave of discontent with President Barack Obama to majority power in both houses of Congress for the final two years of his presidency.

Republicans won Democratic-held Senate seats in Arkansas, Colorado, Iowa, Montana, North Carolina, South Dakota and West Virginia, assuring them of majority control of the Senate for the first time since January 2007, when President George W. Bush had two years remaining.

They also held their majority control of the House of Representatives and looked to add as many as a dozen seats, which would swell their ranks to a level Republicans haven’t achieved since 1949.

The results vividly demonstrated how constituents were frustrated with government, notably Obama, and most saw the country heading in the wrong direction.

Democratic efforts to offset the Republican momentum with gains of their own failed.

In Kentucky, Senate Republican leader Mitch McConnell easily beat Democratic Secretary of State Alison Lundergan Grimes. The Democrats had hopes for a Republican seat in Georgia, but Michelle Nunn fell to Republican businessman David Perdue. And in Kansas, Democrats appeared to be counting on Greg Orman, running as an independent against Sen. Pat Roberts, a Republican. Vice President Joe Biden earlier Tuesday called Orman “an independent who will be with us in the state of Kansas.” It wasn’t enough. Roberts held the seat.

Democrats did hold New Hampshire, where Sen. Jeanne Shaheen turned back a strong challenge from former Sen. Scott Brown. And they stopped the Republicans, at least for now, in Louisiana. Since no one got a majority, Democratic Sen. Mary Landrieu will face Republican Rep. Bill Cassidy in a runoff next month.

But the night belonged to the Republican Party, thanks to a favorable electoral map and a president with dismal approval ratings. McConnell, speaking to supporters, was both defiant and conciliatory.

“Tonight, Kentuckians said we can do better as a nation,” McConnell said in his victory speech in Louisville. “Tonight, they said we can have real change in Washington. Real change, and that’s just what I intend to deliver.”

Democrats were defending 21 Senate seats to the Republicans’ 15. Seven of the Democratic seats were in states that went for Republican presidential nominee Mitt Romney in 2012 against Obama, including Arkansas, Montana, South Dakota and West Virginia.

“This is probably the worst possible group of states for Democrats since Dwight Eisenhower,” Obama said Tuesday in an interview on WNPR in Connecticut.

In House races, two Democratic incumbents fell: Rep. Nick Rahall of West Virginia and Rep. Joe Garcia of Florida. Rahall, first elected to the House in 1976, was the victim of a GOP surge in a state that’s trended increasingly Republican.