President Joe Biden's executive order to require that their employees be vaccinated for COVID-19 by a Dec.

The two Texas-based carriers said the federal mandate superseded an order by Republican Governor Greg Abbott barring COVID-19 vaccine mandates by any entity, including private employers.

Southwest said it "would be expected to comply with the President's Order to remain compliant as a federal contractor." American said while it was reviewing Abbott's executive order, "this does not change anything" for the company.

In his executive order, Abbott said the Biden administration was "bullying" many private entities into imposing COVID-19 vaccine mandates, causing workforce disruptions.