But rival Virgin Atlantic said the proposals were "woefully inadequate" and would lead to higher prices for consumers.
The European Commission gave interested parties a month to comment on the concessions.
The three carriers, members of the Oneworld alliance, want to deepen the pact to take advantage of the U.S./EU "Open Skies" agreement, which liberalises trans-Atlantic aviation.
"If the market test confirms that the proposed commitments remedy the competition concerns, the Commission may adopt a decision ... making the commitments legally binding on the parties," the European Union competition watchdog said.
Such a decision would mean the Commission dropping its investigation and no fines levied on the companies.
Alliances are seen as a lucrative alternative to mergers and large-scale investments.
The Commission said in a statement that the airlines had offered to give up some landing and take-off slots for routes from London to Dallas, London to Boston, London to Miami and possibly London to New York should competitive conditions change.
The carriers also proposed to allow access to their frequent flyer programmes on those routes as well as London-Chicago and Madrid-Miami, and submit data on their cooperation.
"I continue to question why the Commission is even considering these proposals to try and put right the consumer harm of this monster monopoly when it does not seem to have any evidence of concrete consumer benefits," Richard Branson, president of Virgin Atlantic, said in a statement.
Branson, who met Competition Commissioner Joaquin Almunia this week to discuss the issue, said Virgin would attempt to show why the alliance should be stopped.
The Commission opened an investigation into the planned alliance last April.
The airlines want to manage jointly schedules, capacity and pricing as well as share revenues on routes between North America and Europe.
American Airlines, BA, Iberia, Finnair and Royal Jordanian Airlines last month secured tentative approval from the U.S. Department of Transportation (DOT) for their plan to form a global alliance.
The DOT has given interested parties 45 days to object. Answers to objections will take a further 15 days.
BA shares were up 1.4 percent and Iberia was 0.4 percent higher by 1433 GMT, outperforming a 0.33 percent lower Stoxx Europe transport and leisure index.
The Commission is also probing proposed alliances between members of Star Alliance, and members of SkyTeam, both rivals of Oneworld. (Reuters)
