Unite's Joint General Secretary Tony Woodley said serious progress had been made since negotiations resumed after two sets of strikes by cabin crew last month.
The union will not set further dates for strikes while the talks continue to make progress, he added.
However, there is more work to be done, and further discussions will take place with the company over the next few days, Woodley said in a statement.
The traffic numbers reflect the industrial action which took place last month and the impact of that is between 40 and 45 million pounds ($68.55 million), George Stinnes, BA's group treasurer told reporters.
We operated 79 percent of long-haul and 58 percent of shorthaul flights over the two strikes and if there are more (strikes) we would expect to fly a substantial program.
BA's shares closed down 2.1 percent at 238 pence, valuing the business at around 2.8 billion pounds.
Unite had previously warned it would stage more stoppages unless the two sides can come to an agreement on pay and staffing levels among cabin crew.
The strikes were an embarrassment for Prime Minister Gordon Brown, who is trailing the opposition Conservatives in the opinion polls before a May 6 election.
Brown's Labor Party has strong union links and Unite is its main financial backer. Conservative leader David Cameron says Brown has been reluctant to take a tough line with his union backers. No one at British Airways could immediately be reached for comment.
(Reporting by Peter Griffiths and Rhys Jones; Editing by Bernard Orr)