Low-wage workers at the airports want MWAA to require contracting firms pay them $15 per hour.
The suit, filed last month, is similar to other unsuccessful efforts that have challenged the use of toll road revenues to finance the Silver Line rail project.
McAuliffe said the money would be used to make the airport more appealing to the airlines that serve it.
The action runs counter to D.C. Mayor Muriel E. Bowser's efforts to ensure the District has more influence in regional issues.
New rules went into effect Sunday, allowing the popular app-based services to legally operate on airport grounds. But the services are being charged a per-trip access fee, which they have decided to pass on to customers.
Quince T. Brinkley, vice president and secretary at the Metropolitan Washington Airports Authority will leave July 10, after seven years on the job.
Temporary outage Saturday afternoon caused some flight delays.
MWAA is looking for someone to manage the $5.6 billion Silver Line rail project. Think you have what it takes?
The Metropolitan Washington Airports Authority, an entity that for many years played by its own rules, will now be subject to permanent federal oversight.
Still no firm date as to when Metro's new Silver Line will open to the public. Testing on the new rail line is set to start next weekend.