American Airlines said it, Oneworld alliance members and private equity fund TPG would be willing to invest $1.1 billion in Japan Airlines to match a similar bid from rival Delta and the SkyTeam alliance.

American is eager to prevent JAL's defection from Oneworld, as Delta Air Lines said that it could team up with a private equity fund or venture capital firm to offer more than its previously announced $1 billion to JAL.

The two are in an escalating bidding war over the lucrative Asian routes of Asia's biggest airline, which is seeking a state bailout to deal with mounting debt.

American Airlines said on Thursday that the total financial benefit from its backing would be equivalent to $1.8 billion when factoring in an estimated $700 million for the net present value of antitrust immunity over a period of 10 years.

American Airlines has said it would apply for antitrust immunity with JAL under an open skies treaty to liberalize air travel between the U.S. and Japan. The treaty is expected to be agreed upon by the two governments as early as this month.

Delta Airlines President Edward Bastian also told reporters in Tokyo on the same day that it and its SkyTeam partners would be happy to offer more support.

We are putting our capital at risk, not someone else's capital ... I think that's important. However, if the (Japanese) government asks us to go back and raise more capital, we are happy to do so, Bastian told Reuters on the sidelines of a news conference.

Bastian said, however, that the airline has not received such a request.

Delta said on November 18 that SkyTeam member carriers were ready to offer $1 billion, including a $500 million equity investment, in return for JAL defecting from the Oneworld alliance and its partnership with American Airlines.

Shares of JAL were up 1.1 percent, underperforming a 2.8 percent rise in the benchmark Nikkei average.

(Reporting by Nathan Layne and Mariko Katsumura; Writing by Mayumi Negishi; Editing by Edwina Gibbs)