But governments are notoriously reluctant to relinquish control of aviation treaties because they raise issues of national sovereignty and security.
The parties argued that the law conflicted with existing aviation treaties and a swath of other agreements and principles.
Washington and London now have one of the most restrictive aviation treaties in the world.
And these talks have largely been separate from negotiations over the aviation treaty and the transfer of rights at Heathrow, the most popular London airport.
Its 50,000 employees manage a fleet of 312 planes flying to 100 countries, with many areas governed by different aviation treaties.
The two-day session was the third round of talks on the civil aviation treaty between the countries.
The Government could also renounce the aviation treaty, in which case the treaty as it now exists would remain in place for a year.
Over the years, Western democracies have threatened but never imposed sanctions called for in civil aviation treaties to penalize states that sponsor or shelter terrorists.
Japan said that the situation has existed since 1952, when the two nations signed a civil aviation treaty.
A longstanding international aviation treaty limits a carrier's damages to $75,000 per passenger, unless the family proves that the airline's misconduct was willful.