American Airlines and rival Delta are keen for a foothold in Asia
American Airlines and private equity firm TPG have offered $1.1bn (£659m) of investment to struggling carrier Japan Airlines (JAL).
It said the offer was "far superior" to the $1bn offered by rival Delta.
Both carriers are keen for a stake in the Asia Pacific market. JAL has said it will make a decision on the bids by the end of the year.
The Japanese carrier has been struggling with competition, rising fuel prices and huge debts.
Japan's government has bailed it out four times since 2001. The airline lost $1.5bn in the six months to September.
Aviation consultant Mark Kiefer said: "There's a lot at stake here, especially given the importance of the Japanese market and the Asian market to all of these carriers."
American Airlines said its deal would provide $700m in extra revenue and that together they would receive anti-trust immunity.
However, Delta's lawyer Jeffrey Shane has asserted that a JAL-Delta alliance would pose "no threat" to competition.
The BBC's Roland Buerk in Tokyo said Japan Airlines still had plenty of problems to overcome - including massive debts. It is trying to get its staff to accept a 40% cut in their pensions.