British Airways and the Unite union representing cabin crew have resumed talks amid the third day of the latest industrial action.
Unite joint leader Tony Woodley said "it will not be easy" to reach a settlement.
Earlier, BA had said it was planning for a full hearing on the legality of the strike, despite a court ruling in favour of Unite last week.
BA stressed that it was not appealing against that decision.
A long-running dispute over pay, working conditions and perks has seen both industrial action and talks involving the two sides.
The last set of talks were broken up when left-wing activists from the Socialist Workers Party managed to interrupt a meeting between the company and the union.
Some 246 flights in and out of Heathrow were cancelled on Wednesday out of 674 scheduled.
On Tuesday, more than 200 flights were cancelled, though BA maintained that it was meeting its target of flying 70% of passengers to their destinations.
BA said it was increasing its flight schedule for Unite's next threatened five-day strike, which is due to start on Sunday.
The carrier said it would be operating more than 70% of long-haul flights from Heathrow and more than 55% of short-haul flights.
"I really hope we pick up the momentum of the talks from where we were on Saturday before we were invaded by the Socialist Workers Party," Unite's Mr Woodley earlier told the BBC.
Mr Woodley said Saturday's meeting was the first time that he "genuinely thought there was a bit of effort going in to settle this".
He also called for BA to restore travel concessions to workers who had previously gone on strike.
BA's chief executive Willie Walsh has previously expressed his frustration that previous agreements with Unite's leadership have been rejected by the Bassa arm of the union, which directly represents BA cabin crew.
BA's legal challenge still revolves around whether Unite did enough to communicate the results of the strike ballot to its members.
A BA spokesman said the prospect of a full court case was always on the cards.
"The union would have been fully aware that the point of law over the communication of the strike ballot result would come to a full court case in due course," he said.
He added that BA had written to the Unite union, which represents the crew members, reminding them to keep all relevant paperwork, pointing out that this was standard procedure for pending court cases.
Unite said negotiation, not litigation, was the way to solve the dispute.
"Two of the three most senior judges in the land concluded last week that if BA pursued its case for full hearing, the court would highly probably back the union," Unite said in a statement.