The two airlines said the federal mandate supersedes Abbott's order, and have asked all their U.S.-based employees to submit vaccination proof by November 24.
Southwest said it would be expected to comply as a federal contractor, while American said Abbott's order would "not change anything" for the company.
Vaccine mandates have become a flashpoint in U.S. politics, with critics are calling them unconstitutional and authoritarian.
Six United Airlines employees have filed a lawsuit claiming that workers who sought vaccine exemptions were subjected to intrusive inquiries about their medical conditions or religion, including requiring letters from pastors.
The federal court issued an order on Tuesday temporarily restraining United from placing any employee who receives vaccine exemptions on unpaid leave and denying any late exemption requests.
Abbott has said the Biden administration was quote "bullying" many private entities into vaccine mandates, causing workforce disruptions.
In its response, the White House said on Tuesday that Abbott's order was out of step with businesses in the state, and that the governor's decision was motivated by politics, not science.
