'Bring 'em on': Most profitable airline Delta wants United's crown over the Pacific, too.

United Airlines and Delta Airlines jets

Sam Hodgson | Bloomberg | Getty Images

RIO DE JANEIRO — Delta Air Lines is the nation's most profitable carrier, but its hungry rival, United Airlines, is far bigger over the Pacific. Delta's new president, Peter Carter, says that just won't stand.

"We want to become stronger, better, faster in the trans-Pacific, and we want to become the leading U.S. carrier" across the Pacific, Carter told CNBC in an interview here during the International Air Transport Association's annual meeting. "Ultimately ... the real goal is to become the leading global carrier, which is a pretty audacious goal."

Carter, who was promoted in March, said some of that will come from Delta's joint venture with Korean Air, which is merging with Asiana Airlines.

Delta posted a net profit of more than $5 billion last year, compared with United's earnings of about $3.35 billion. However, for its trans-Pacific business, Delta's smaller network generated just $2.79 billion in revenue, compared with United's roughly $6.89 billion, according to company filings.

Trans-Pacific flying is often highly profitable, with long-haul flights commanding a premium and served by planes with dozens of premium seats.

Both carriers are adding new routes. Earlier this month, Delta launched nonstop service between Los Angeles and Hong Kong. United Airlines, meanwhile, is planning a nonstop between its San Francisco hub and Sapporo, Japan — a play for premium-ski traffic.

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Delta and United account for most of the U.S. airline industry's profits.

Delta spent the better part of the last two decades fashioning itself the luxury airline of the U.S., from high-end lounges to a lucrative partnership with American Express.

United has launched its own campaign using similar tactics, including a heavy investment in technology, massive aircraft orders, and an international network with new destinations from Mongolia to Croatia to Greenland.

The U.S. air travel market — the world's largest — is mature, meaning there's little room for significant annual growth. "Really, when we think about the future, it's all about international," Delta's Carter said.

United CEO Scott Kirby said Sunday that he was flattered by Delta's ambitions.

On the sidelines of the same conference, Kirby said he has "a lot of respect for Delta, and what they have done, and I take it as a huge compliment that Delta is beginning to acknowledge that they have an equal that they're worried about and trying to compete with us."

When asked what he wants to beat Delta on, Kirby replied: "Everything."

Carter said in the interview that Delta can't rest on its current success.

"We always have to be hungry to win, and I say that because I know United is out there competing against us and replicating the playbook a little bit," he said. "Bring 'em on."