DALLAS (AP) -- American Airlines is turning on the charm as it attempts to persuade Japan Airlines Corp. to strengthen their relationship instead of running off with a new suitor, Delta Air Lines Inc.

In recent days, the CEO of American parent AMR Corp. visited Tokyo to meet with his JAL counterpart, and the chief financial officer will go there next week, AMR officials say.

American's pitch is simple: Stay with us and things will get better. Go with Delta and you never know what might happen.

American says if JAL switches from the oneworld alliance of global airlines to Delta's SkyTeam alliance, it would cost JAL up to $500 million in lost revenue in the first two years after the changeover.

That figure assumes Delta initially will only be able to replace about half the revenue-sharing and other money that JAL currently gets from its oneworld partners, including American, based in Fort Worth, Texas.

On top of that, American officials say, if JAL sticks with them, they could both apply for antitrust immunity from U.S. and Japanese regulators and bring in up to $100 million a year in additional revenue. Such a tie-up would depend on U.S. and Japanese government officials striking a so-called open skies agreement that would reduce barriers to airlines from one country operating in the other.

Delta officials declined to comment on Friday, although privately they disputed American's figures.

Delta is likely to argue that JAL will suffer far less disruption than American suggests if it switches alliances. After all, JAL already has agreements to sell tickets on each other's flights with several of Delta's SkyTeam partners, including Air France, Alitalia, Korean Air and China Southern Airlines.

Atlanta-based Delta has also sent several high-level executives, including president Ed Bastian, to Japan to press its case with JAL officials.

Both U.S. carriers are drawn to financially troubled JAL because of its valuable network of routes in Asia.

Kenji Hashimoto, AMR's vice president of alliances, said in an interview Friday that JAL "is in a very tough financial situation right now. Any kind of switch introduces a lot of risk."

For example, Hashimoto argued, if JAL goes with Delta, then Delta's SkyTeam alliance -- which also includes Northwest Airlines with its frequent service to Japan -- would control 62 percent of the Japan market. That, he said, would make regulators unlikely to grant antitrust immunity to a JAL-Delta tie-up.

Patrick Murphy, a former high-ranking official in the Transportation Department, said Delta would have more trouble winning regulatory approval for antitrust immunity because it already has a large share of the U.S.-Japan travel thanks to Northwest.

JAL officials "have to be factoring what are the prospects of getting approved," said Murphy, who is now an airline consultant but says he is not working for American, Delta or JAL.

Delta partisans argue that even combined with JAL's flights, Delta and JAL would have a smaller share of the U.S.-Tokyo market than American and partner British Airways enjoy on flights between the U.S. and London's Heathrow Airport. American and BA are asking for immunity to work more closely on that trans-Atlantic service.

American and Delta have offered to make investments in debt-burdened JAL, which announced this week it would eliminate 17 routes by next June to save money.

American serves Japan from four U.S. airports: Dallas-Fort Worth, Los Angeles International, Chicago's O'Hare and New York's Kennedy.

Delta and its Northwest subsidiary fly year-round to Japan from nine U.S. cities, including New York, Los Angeles, San Francisco, Seattle and Atlanta.