No fare hike if...: CEO of new American Airlines

American Airlines CEO: Done deal and set to fly
American Airlines CEO: Done deal and set to fly

Now that American Airlines and US Airways have completed their merger to become the nation's largest air carrier, it's hard to say whether the industry consolidation trend will take a pause, CEO Doug Parker told CNBC on Monday.

He also promised that fares won't rise "as long as demand stays the same."

American as well as United and Delta have global strength with access to the main business centers of the world. So airline competition will be based on how good the in-flight experience is for travelers, Parker said on CNBC's "Squawk Box."

Cramer: AAL merger is good for the consumer
Cramer: AAL merger is good for the consumer

"The three of us have now the ability to take people pretty much anywhere in the world. What used to be a business where it was purely on schedule, if you have the ability to take people everywhere, you have to compete on product. And we're prepared to do that," said Parker, who had been the CEO of US Airways before the merger.

The newly combined carrier began trading Monday morning under the ticker symbol AAL.

With American Airlines coming out of bankruptcy with this merger, Parker said, airlines that aren't profitable won't be able to grow. "We expect to produce a profit that will provide a nice return for our investors. That's what they expect. And that's what we plan to deliver."

The new company's modern fleet will give it a competitive edge, he continued, adding that nothing about this transaction will affect air fares because the carriers are highly complementary. "We're keeping all the airplanes, keeping all the people. So supply should be unchanged. As long as demand stays the same, nothing should happen to prices."

Andrew Harrer | Bloomberg | Getty Images

The U.S. Supreme Court refused to grant a stay on Saturday night that would have stopped the merger. The stay had been requested by a group of consumers and travel agents who said the merger would cause "irreparable" injury to the domestic airlines industry.

(Read more: Supreme Court justice denies stay in airline merger)

The newly combined airline faces a tough Monday because of the ice storm that slammed the Southwest on Friday, bringing the northern part of Texas to a standstill, and leading to massive flight cancellations at the busy Dallas/Fort Worth International Airport.

"It's been an extremely rough weekend for our employees and our customers," Parker acknowledged, noting the bad weather, but said the cost of all the canceled flights won't be "overly material" to the airline's bottom line.

By CNBC's Matthew J. Belvedere. Follow him on Twitter @Matt_SquawkCNBC. Reuters contributed to this article.