ATLANTA (AP) — Michelle Nunn has won the Democratic nomination for a crucial U.S. Senate seat in Georgia and now awaits the winner of a fiercely contested GOP race.

The Georgia race is among a dozen being watched nationally, as Republicans make a push to claim a majority in the Senate. Democrats consider Georgia a state where they could thwart GOP plans to pick up six additional seats, and Nunn — the daughter of former Sen. Sam Nunn — has proved to be a formidable fundraiser.

In early returns Tuesday, Nunn showed a sizable lead. Also on the ballot were former state lawmaker Steen Miles, psychiatrist Branko Radulovacki and ROTC instructor Todd Anthony Robinson.

The crowded GOP race, meanwhile, remained too close to call Tuesday evening.

Copyright 2014 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.