While the company declined to put numbers on the delays, research firm ShipMatrix said last week that 89 percent of UPS Express packages were delivered on time. It expects to be back to normal operations by the end of Wednesday.
Along with rival FedEx Corp., UPS has benefited greatly in recent years from the growth in online shopping.
"UPS is likely to see cost pressure and the company has had past execution issues regarding holiday deliveries", wrote CFRA Research analyst Jim Corridore, referring to December stumbles in previous years.
The U.S. Postal Service, which delivers more online orders to residences than anyone, is expanding delivery hours to handle the peak season's volume, with packages delivered early in the morning, evening and on Sundays. A record $6.59 billion was spent online overall, according to Adobe Analytics data. But, he added, "UPS needs to make sure packages do not miss Christmas day". UPS has underperformed the market so far this year, up 5 percent versus the S&P 500's 18 percent since January.More news: Pizza Hut tests beer and wine delivery
The seasonal challenges have been compounded by the fact the improving economy has made it more hard - and expensive - to find seasonal help.
"We are taking all necessary steps to ensure we are serving our customers' demand, especially during this holiday period", Gaut said. It has notified workers at more than 100 package-delivery centers where demand is highest that it may raise the number of hours drivers work to 70 hours over an eight-day period, up from 60 over seven days.
The Teamsters union, which represents 250,000 UPS employees, isn't happy with that plan.
This year, UPS brought on 95,000 seasonal workers for the holidays.