WASHINGTON — Bob Kerrey won the Democratic nomination for Nebraska’s open U.S. Senate seat Tuesday while Republicans decided a tight three-way race that reflected the divisions within the GOP.

Kerrey, a former senator seeking another turn on Capitol Hill in one of the year’s most contested races, easily captured the Democrats’ nomination.

Nebraska state Sen. Deb Fischer won the Republican nod for U.S. Senate, setting the stage for a high-stakes November election against Kerrey. The 53-year-old Fischer overcame low name familiarity and being outspent by two competitors to win the nomination in Tuesday’s election. She was backed by Sarah Palin and former candidate Herman Cain.

The race has drawn national attention because a GOP win would push Republicans closer to a Senate majority. Nebraska is a solidly Republican state, but Democrats think they have a shot of winning with Kerrey, a former senator, governor and presidential candidate. Kerrey easily won the Democratic nomination. The general election winner will replace Democratic Sen. Ben Nelson, who isn’t seeking a third term.

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Nebraska and Oregon Republicans have made clear their preference for the GOP nomination by choosing Mitt Romney in Tuesday’s presidential primaries.