American Airlines is digging deeper to save its relationship with Japan Airlines, with sources saying it has raised the amount it is willing to invest in the troubled carrier by $300 million.

American's total offer has now reached $1.4 billion in a battle with Delta Air Lines Inc. Delta wants to create a close partnership with Japan Airlines that would operate across the Pacific and throughout Asia.

American executives told Japan Airlines, or JAL, of its new offer on Thursday, according to two people close to the situation in Tokyo, who spoke on condition of anonymity because the talks were confidential.