JetBlue Airways Corp. (JBLU) said on Tuesday it would cost $30 million or more to reimburse the 130,000 or so passengers affected by canceled flights over the past six days and to meet extra costs caused by the cancellations.

"It's going to be very expensive," CEO David Neeleman said in a TV interview. "I don't have the final number, but it's going to be maybe $20 million or $30 million and maybe a little bit higher."

Neeleman said the costs would hit first-quarter results and JetBlue would update its financial forecasts soon.

The embattled airline made the first moves toward rebuilding its tarnished reputation when it introduced a customer bill of rights and new procedures for handling operations disruptions on Tuesday. The announcement came as the company returned to normal operations for the first time after nearly a week of weather-induced woes.

Click Here to See More of the Bill of Rights.

Among the 'rights' announced by the company are payments in the form of vouchers to passengers who are delayed "in a situation within the company's control," or who are unable to de-plane after landing. The compensation would increase with time, so that a passenger delayed for shorter periods might receive a $25 voucher, while a traveler held for 4 hours and longer could be compensated with an entire round-trip voucher.

The airline also said that in the case of aircraft ground-delayed more than 5 hours, the airline would take action to deplane passengers, unless takeoff were imminent.

"This will be a living document. We'll continue to add to it," JetBlue founder and chief executive David Neeleman told FOX & Friends on Tuesday morning.

Neeleman also sought to re-establish and emphasize JetBlue's reputation as an industry pioneer, saying "JetBlue is a different sort of airline. We're so customer service focused and we always have been."

Speakout! Do you think JetBlue's new Customer Bill of Rights will fix their public relations blunder? Click here to tell us!

The onslaught of angry and disgruntled travelers at JetBlue's terminal at John F. Kennedy International Airport, its New York hub, appeared to ease on Monday as service desks functioned more smoothly. Customer calm prevailed despite the cancellations of 139 of 600 scheduled flights at 11 other airports.

Last week's snow and bitter cold temperatures froze equipment and grounded the company's planes at Kennedy, stranding passengers inside them for up to 10 1/2 hours. JetBlue, which prides itself on low fares and great customer service, said it waited too long to call for help in getting the passengers off the planes because it hoped the weather would let up and the flights would be able to proceed.

The weather delays and cancellations led to customer questions and complaints that overwhelmed the company's reservations system, and many of its pilots and flight crews wound up stuck in places other than where they were needed.

Monday's cancellations gave the airline time to get equipment to the proper places and helped make sure all flight crews had legally mandated amounts of rest before flying again, JetBlue spokesman Sebastian White said. Planes were being repositioned on Monday to be ready to go on Tuesday morning, he said.

When the bad weather struck Feb. 14, JetBlue didn't have a system in place for many stranded flight crews to call in to be rerouted, something the airline is working to rectify, Neeleman said. The service breakdown "was absolutely painful to watch," he said Monday.

One travel expert suggested the airline had brought the crisis on itself by trying too hard to accommodate its passengers.

"Most airlines don't try to operate when there is an ice-storm problem — they've learned that it's better to cancel all flights at the outset and then try to get back to normal operations as quickly as possible," said David Stempler, president of the Washington-based Air Travelers Association.

Stempler said the fast growth of airlines such as JetBlue can create demands that are beyond their capability, especially in crises.

"JetBlue tried to do their best — tried to keep the system rolling," he said. "Their heart was in the right place, but their head was not."

Monday's cancellations affected flights at airports in Richmond, Va.; Pittsburgh; Charlotte and Raleigh/Durham, N.C.; Jacksonville, Fla.; Austin and Houston, Texas; Columbus, Ohio; Nashville; Portland, Me.; and Bermuda.

Reuters, the Associated Press and FOXNews.com's Alexander B. Duncan contributed to this report.