Abbott, a Republican, told conservative radio host Glenn Beck on Tuesday that the NFL "is walking on thin ice" with its veiled threat.
After criticizing the NFL for allowing players to kneel during the national anthem, Abbott said: "The NFL needs to concentrate on playing football and get the heck out of politics."
On Friday, in response to an email question about the Texas bill, which was filed last month, league spokesmanBrian McCarthy said: "If a proposal that is discriminatory or inconsistent with our values were to become law there, that would certainly be a factor considered when thinking about awarding future events."
Said Abbott on Tuesday: "For some low-level NFL adviser to come out and say that they are going to micromanage and try to dictate to the state of Texas what types of policies we're going to pass in our state, that's unacceptable.
"We don't care what the NFL thinks and certainly what their political policies are because they are not a political arm of the state of Texas or the United States of America. They need to learn their place in the United States, which is to govern football, not politics."
Abbott had responded to McCarthy's statement on Twitter on Saturday, indicating he wasn't threatened by it and pointing to the Deflategate case as an example of the NFL's hypocrisy.
The NFL has selected future Super Bowl sites through 2021, none of which are in Texas. Dallas hosted the game in 2011, and three Super Bowls have been played in Texas since 2004, which is second only to Florida.
Under the Texas bill, people would be required to use bathrooms that correspond to the sex on their birth certificate. It's similar to a North Carolina law that prompted the NBA to relocate the All-Star Game from Charlotte to New Orleans and the NCAA to pull seven championship events from that state last year.
The bathroom bill is backed by Republican Lt. Gov. Dan Patrick, a powerful figure in Texas who had cited the Houston Super Bowl as proof that big events will stick around. Following the NFL statement, Patrick's office signaled on Friday that it was remaining firm and was committed to "making sure that every Texan is welcomed" at sporting events.
Unlike the North Carolina law, the Texas proposal stops short of some provisions the NCAA singled out when defending its decision to relocate events this past fall. That includes language that invalidates local equal-rights ordinances, although there is separate legislation in Texas that could have similar effects.
The NFL has issued similar warnings before about state legislation that critics say invites discrimination. In 2016, Georgia Republican Gov. Nathan Deal vetoed a "religious liberty" bill that the NFL suggested could result in Atlanta being passed over for Super Bowls.
The Associated Press contributed to this report.