Abbott on Proposition 1: "The Issue's Not Over"

^{*Editor's note: This story has been updated throughout.}

Gov. Greg Abbott said Monday the fight is not finished when it comes to regulations in Austin that have driven ride-hailing companies out of the state capital. 

"The issue's not over," Abbott said in an interview on CNBC. "Republicans in the Texas Legislature have already raised proposals coming up in the next session to override the Austin vote." 

Pressed on whether ride-hailing companies Lyft or Uber would return to Austin, Abbott said: "I'd just say the game is not over. It's halftime, and we'll see what happens in the second half."

The remarks were Abbott's first public comments on Proposition 1. Austin voters defeated the measure earlier this month, keeping in place more stringent rules for ride-hailing companies, such as fingerprint background checks. Lyft and Uber suspended their operations in Austin shortly after the May 7 vote. 

Outraged by what they see as local control run amok, some state lawmakers are vowing to revisit the issue during the 2017 session. State Sen. Charles Schwertner, R-Georgetown, has promised to file legislation next year "designed to establish consistent and predictable statewide regulation of ridesharing services."

Read MoreTop Texas Senator Announces Ride-Hailing Legislation

In the CNBC interview, Abbott was read a tweet from venture capitalist Paul Graham that said "Austin has zero chance of being a serious startup hub without Uber and Lyft." Abbott denied that, saying the city is "already a dynamic startup hub."

"That process has already left the barn, as we say in the state of Texas, and there's nothing that will slow it down," Abbott said. "And the dynamics that's causing Austin to be a startup hub are already in place and will not be diminished by" the Proposition 1 vote.

In another media appearance Monday, Abbott spoke highly of Uber, agreeing with a host's suggestion that the service is "good for America." 

"It provides options for Americans, and I think that's a good thing," Abbott told Bloomberg Politics' Mark Halperin.

Abbott is currently in New York to promote his new book, "Broken But Unbowed." He heads off to tout the book on a bus tour of Texas on Wednesday.

Disclosure: Uber and Lyft have been financial supporters of The Texas Tribune. A complete list of Tribune donors and sponsors can be viewed here.