(Reuters) - Democratic Texas State Senator Wendy Davis, whose June filibuster over proposed abortion restrictions captured national attention, said on Wednesday that she would announce on October 3 whether she would seek the governor's office.

Davis, 50, would face an uphill battle to become the first Democrat to win statewide office in Texas since 1994 against Republican state Attorney General Greg Abbott.

Governor Rick Perry is not seeking re-election.

"There's one question I've gotten quite often in the past few months, Davis said in an email statement to supporters. "I've heard it online, while I'm traveling around the state, from the media, and in my Fort Worth neighborhood: What's next?"