The party so far has picked up Democratic-held seats in Colorado, Montana, South Dakota, Arkansas and West Virginia.
The Republicans, who already control the House of Representatives, need to gain just six seats to take the Senate.
They will take Senate control with one more seat provided they don't lose any seats they now control. But races in GOP-held Georgia and Kansas remain tight.
The election shaped by widespread voter discontent with Obama could complicate his last two years in office, reducing his room to maneuver but also potentially opening new areas for compromise.
As polls close across the country, early results indicate a number of both Democratic and Republican Senate incumbents have held onto their seats.
One of the key early results came in Kentucky, where Republican Senate Minority Leader McConnell fended off Democrat Alison Lundergan Grimes, positioning himself to lead the chamber should the Republicans win the majority.
Indian-American governor of South Carolina Nikki Haley has registered a convincing win over her nearest Democratic rival Vincent Sheheen to win a second term. The victory has boost her profile in the Republican party at the national level.
Projections show Republicans have retained seats in Alabama, Georgia, Kansas, Maine, Mississippi, Nebraska, Oklahoma, South Carolina and Tennessee.
Democrats have retained seats in Delaware, Massachusetts, New Jersey and Rhode Island.
They have also held on to the key Senate seat of New Hampshire. The elections likely to expand the House Republican majority, potentially to its largest size in decades.
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