UPS and FedEx, normally rivals, are working side by side to ship the coronavirus vaccine developed by Pfizer and BioNTech, the first of the vaccines to win U.S. government approval.

The two shipping companies said they had put plans they had been working on for months into action after the Food and Drug Administration gave the vaccine emergency authorization late Friday.

Delivery of the first vaccines comes as the virus continues to rage across America, with officials reporting more than 207,000 new cases on Saturday. That brought the total number to more than 16 million, by far the most in the world, less than a week after the country surpassed 15 million. More than 3,000 deaths were reported for the first time on Wednesday, and the country’s total is approaching 300,000.

At a news conference on Saturday, Gen. Gustave F. Perna, the chief operating officer of Operation Warp Speed, the federal effort to bring a vaccine to market, said that boxes were being packed at Pfizer’s plant in Kalamazoo, Mich., and would be shipped to UPS and FedEx distribution hubs, where they would be dispersed to 636 locations across the country. Pfizer said shipping would start early Sunday morning.

Mr. Perna specified that 145 sites would receive the vaccine on Monday, 425 on Tuesday and 66 on Wednesday.

“Make no mistake, distribution has begun,” he said.

UPS said it expected to start transporting the vaccine on Sunday morning, when employees stationed at Pfizer’s facility in Michigan will affix special Bluetooth- and radio-enabled tracking tags to each shipment. An aircraft waiting nearby will take the vaccine to the company’s Worldport air cargo hub in Louisville, Ky., a sprawling 5.2-million-square-foot sorting facility. Future shipments of the vaccine will also be transported by truck to the Louisville hub, which is up to a six-hour drive from Michigan.

“This is the moment we’ve been waiting for,” Wes Wheeler, president of the company’s health care division, said in an interview on Saturday. “We’ve been planning for months with daily calls, drilling down to really quite minute details.”

Mr. Wheeler said he planned to oversee the first vaccine shipments from a newly established 24/7 command center in Louisville, which will be staffed at any given time by teams of five to 10 people who will monitor each vaccine package as it moves through the UPS network.

Once the vaccine shipments arrive at the Louisville hub, they will be sorted alongside other packages and distributed to hospitals and other medical facilities. Every truck driver or airplane pilot will know if they are carrying a vaccine package, Mr. Wheeler said. Both UPS and FedEx have said that doses will arrive at their destinations a day after leaving the Pfizer facilities.

Even before the vaccine was approved, UPS had already started shipping out kits with the medical supplies needed to administer it, such as alcohol wipes and syringes, Mr. Wheeler told a Senate subcommittee this week.

UPS and FedEx will split distribution of the vaccine throughout the country. After those shipments arrive, all Pfizer dosing sites will receive another shipment from UPS of 40 pounds of extra dry ice to keep the vaccines at a frigid temperature, he said.

“You have two fierce rivals here, and competitors, in FedEx and UPS, who literally are teaming up to get this delivered,” Richard Smith, a FedEx executive, told the Senate’s Subcommittee on Transportation and Safety on Thursday.

Both companies said the shipments would be closely tracked and monitored, and would be given priority over other packages. To ship its vaccine, Pfizer designed specialized containers packed with enough dry ice to keep a minimum of 975 doses cool for up to 10 days. Each comes with a tracking device.

Like UPS, FedEx said it would also affix its own tracking tags to vaccine shipments. Each UPS truck carrying the doses will have a device that tracks its location, temperature, light exposure and motion, Mr. Wheeler told the senators. The company’s trucks will have escorts, too, he said on Thursday. It is not clear whether he meant the local police or other government officials, or possibly private guards, and he declined to elaborate on that and other details in the interview, citing security concerns. But the trucks leaving Pfizer’s facility will be tracked “by the minute,” he said.