Story highlights "Alabama voters elected a senator who'll make them proud," Clinton tweeted

The race had remained neck-and-neck for the majority of election night

Washington (CNN) Following Democrat Doug Jones' projected win in Alabama's US Senate race, Hillary Clinton shared a message of optimism with her followers on Twitter.

"Tonight, Alabama voters elected a senator who'll make them proud," Clinton tweeted Tuesday night. "And if Democrats can win in Alabama, we can -- and must -- compete everywhere. Onward!"

Tonight, Alabama voters elected a senator who'll make them proud.



And if Democrats can win in Alabama, we can -- and must -- compete everywhere.



Onward! — Hillary Clinton (@HillaryClinton) December 13, 2017

Jones edged out Republican Roy Moore in a race that remained neck-and-neck for the majority of election night.

Jones' win comes after a contentious fight to fill now-Attorney General Jeff Sessions' former seat, with Moore facing several sexual allegations from years ago.

Multiple women accused Moore of pursuing relationships with them when they were teenagers and he was in his 30s, and some of them accused him of sexual assault or abuse.

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