New York CNN Business  — 

United Airlines announced Tuesday that only 593 of its workers face dismissal for not complying with the requirement to get a Covid-19 vaccine. That is less than 1% of its 67,000 US workers who are covered by the rule.

About 2,000 other employees, or less than 3% of the workforce, have applied for a medical or religious exemption from the vaccine, and their cases are now being considered by the airline.

“Our rationale for requiring the vaccine for all United’s US-based employees was simple – to keep our people safe,” said United CEO Scott Kirby in a letter sent to United employees, which was also released to the media. “The truth is this: everyone is safer when everyone is vaccinated, and vaccine requirements work.”

Some of the 593 employees who have not yet complied with the requirement could still be kept on staff if they have received the vaccine or started the vaccine process and had not forwarded proof to the airline.

Some employers are concerned that mandating their staff get a vaccine could lead people to quit their jobs during a very tight labor market. But the jobs at United, almost all of which are covered by union contracts, are apparently attractive enough for even vaccine-hesitant employees to get vaccinated.

Support for employer mandates has also been growing as Covid-19 cases and deaths surged this summer, primarily among unvaccinated people. A CNN poll conducted in August showed 54% supported employer vaccine mandates, up from only 46% support in April.

United, like all airlines, trimmed its staff in 2020 as air travel fell sharply. Airlines are now all in the process of hiring staff to deal with a rebound in air travel. And United officials said some of the most qualified candidates volunteered that they were applying for jobs at United because of the vaccine requirement and what it says about the airline’s commitment to the safety of employees.

United has one of the strictest employer vaccine mandates. The federal employer mandate rules announced by President Joe Biden earlier this month that covered most businesses with 100 or more employees gave workers a choice between vaccination or weekly Covid testing. But there is not a testing alternative for United employees.

The major unions at United have not fought the airline’s vaccine mandate. But Tuesday the pilots unions representing pilots at American and Southwest voiced objections to federal rules they fear could require vaccine for their members.

The Allied Pilots Association, which represents American’s pilots, wrote to 15 high-ranking US government officials saying “mandatory vaccinations could result in labor shortages and create serious operational problems for American Airlines and its peers” at the height of the holiday travel season. It warned of “a scenario in which airlines are forced to either offer unpaid leaves of absence or, worse, implement mass terminations of unvaccinated pilots.”

The Southwest Airlines Pilots Association said it is the union’s belief that it is “each pilot’s right to choose” whether to get vaccinated.

But the federal rules only require employers to mandate either a vaccine or weekly Covid tests, although an employer can chose to have a tougher policy as United has done.

So far the other major US airlines — American Airlines (AAL), Delta (DAL) and Southwest (LUV) — do not have a mandate, although Delta (DAL) has told employees they’ll have to pay more for health insurance if they are not vaccinated.

Both the American and Southwest pilots unions have been voicing displeasure with work conditions at the airlines in recent months for issues that have nothing to do with vaccines. Both unions have announced plans to hold informational pickets of the airlines later this year, though in neither case would they engage in a work stoppage.

United had planned to place employees who had medical reasons for not getting the vaccine on medical leave, which could include partial pay, depending upon the terms of their union contract. And it planned to place those whose requests for religious exemptions were accepted on unpaid leave. Those who had applied for those exemptions and had the requests rejected would face dismissal.

Six United employees who had applied to be exempt from the mandate for medical or religious reasons, if not both, filed federal lawsuit last week challenging the mandate. In response, United put on hold plans until at least October 15 to place those with exemptions on leave and to dismiss those whose request for exemption had been rejected.

While United is a strong supporter of employer vaccine mandates, it does not support the idea of requiring passengers to be vaccinated in order to fly.

“I don’t think [mandating vaccination for] air travel on its own will drive a huge increase in vaccination rates,” Kirby told CNN earlier this month. “I think this employer mandate will drive a really big increase.” He said he was concerned passenger mandates risked “creating friction in airports, friction in subways, friction across the board.”

– CNN’s Pete Muntean and Gregory Wallace contributed to this report