"Understand this, there's only one body of the three branches of government that can write the law and that is Congress," Abbott said on Fox News' "Fox and Friends." "We have a president who decided, well, if Congress is not going to pass the law, he's going to impose the law. And so the President is turning the Constitution on its head."
Abbott charged that Obama is making executive decisions because he's in the "waning months" of his presidency.
"He's trying to cram down as many parts of his liberal agenda on the United States of America as he possibly can," Abbott said.
Abbott also said Hillary Clinton is nothing more than an "extension of the Obama agenda, if not worse."
In an earlier interview Monday on MSNBC's "Morning Joe," Abbott said he will support the Republican nominee for president, who he expects will be Donald Trump.
"We do have a choice, it's not like 'none of the above' is a potential option," he said. "Texans will robustly come out and support a campaign against Hillary Clinton ... Donald Trump is going to win the state of Texas."
Abbott's comments on the transgender bathroom issue come after the White House issued guidance last week directing public schools to allow transgender students to use bathrooms matching how they self-identify their gender. If schools don't follow the guidance, they risk the loss of federal funding.
The White House is in a heated legal standoff with North Carolina over its controversial House Bill 2
, part of which has to do with transgender bathroom access.
CNN reached out to the Obama administration for comment on Abbott's remarks Monday. On Friday, White House press secretary Josh Earnest defended the guidance, saying it came after the "extensive requests for guidance and for information and advice that have been put forward by school administrators and teachers."
"It is my strongly held belief -- and I'm pretty sure I'm going to be right about this -- that the vast majority of schools and school districts and school administrators across the country will welcome this guidance and will implement it," Earnest said when asked about Republican opposition to the guidance. "For those that don't, there's an established process for them to raise any concerns that they may have."