Southwest Airlines CEO Gary Kelly told CNBC on Tuesday he believes businesses should not impose Covid vaccine mandates on their employees, but he said his company is doing so to comply with federal rules put in place by the Biden administration.”I’ve never been in favor of corporations imposing that kind of a mandate. I’m not in favor of that. Never have been,” Kelly said in an interview on “Squawk on the Street.” “But the executive order from President Biden mandates that all federal employees and then all federal contractors, which covers all the major airlines, have to have a [vaccine] mandate … in place by Dec. 8, so we’re working through that.”Southwest said last week that its 56,000 employees needed to be vaccinated against Covid by Dec. 8 in order to keep working at the airline under the federal mandate. Southwest’s announcement came a few days after other carriers — including American Airlines, Alaska Airlines and JetBlue Airways — informed employees about the need to adhere to federal vaccine rules.In August, before the Biden administration’s action, United Airlines and Hawaiian Airlines instituted Covid vaccine requirements for their staffs. United said earlier this month that more than 96% of its 67,000 U.S. employees have shared proof of vaccination after its late September deadline.Southwest started to offer incentives such as extra pay to spur uptake of the coronavirus vaccine in mid-September, following in the footsteps of other carriers such as Delta Air Lines, American and United.Delta later said that starting Nov. 1 unvaccinated workers would have to pay an extra $200 per month for company health insurance.Kelly noted Southwest’s efforts to encourage employees to receive a Covid shot, adding that individuals also are able to apply for religious and medical exemptions.”My goal, obviously, is that no one loses their job. The objective here, obviously, is to improve health and safety, not for people to lose their jobs,” said Kelly, who’s retiring in February and handing the reins to three-decade Southwest veteran Bob Jordan.Kelly’s comments Tuesday come as Southwest faces heat for widespread flight cancellations in recent days and Monday’s sharp decline in the company’s stock price.There were signs that Southwest’s operations were improving Tuesday, as 87 flights, or just 2% of its schedule, were canceled. Its shares were up about 1%.From Saturday through Monday Southwest scrapped about 2,200 flights, with more than half that number on Sunday alone.According to Southwest, the cancellations can be traced to bad weather and issues with air traffic control in Florida. That caused planes and crews to be in the wrong position, escalating into more pervasive problems. In August, the airline reduced its schedule in hopes of fixing operational struggles over the summer that regularly led to dozens of cancellations.In the past couple of days, the company pushed back on speculation that the recent disruptions were related to workers calling out sick as a way to protest its decision to institute a Covid vaccine requirement.Kelly also denied that was the case in Tuesday’s CNBC interview: “We have some very strong views on that topic, but that’s not what was at issue with Southwest over the weekend.”Kelly has repeatedly urged his staff to get vaccinated. “[But] I do not believe it is up to me, as CEO of a company, to mandate to people that they get vaccinated,” he said in an employee message last month. “That’s my personal philosophy and my personal belief.”— CNBC’s Leslie Josephs contributed to this report.