Earlier the British Airline Pilots Association (BALPA) had said that BA pilots could call off proposed strikes set for Sept. 9 and 10 if the airline agreed to come back to the negotiating table.
But British Airways said the new BALPA proposal would cost an additional 50 million pounds and slammed the union's "new and unrealistic demands".
No further talks between the sides are planned at the moment.
"We remain open to constructive talks with BALPA to resolve the pay negotiations, but we do not believe the union is acting in good faith by making an eleventh hour inflated proposal," the airline said in a statement.
BALPA said last month that the pilots would go on strike for three days in September in a dispute over pay that could disrupt the peak holiday season.
The pilots overwhelmingly voted for industrial action in July and the airline, which is part of IAG, failed in a court bid to stop them.
BALPA has said that British Airways should share more of its profits with its pilots. The union has also given notice to the airline that it will call on its members to strike on Sept. 27.
"Our members' resolve is very strong and they remain very angry with BA, but they also want to leave no stone unturned in trying to find a resolution to their dispute," BALPA General Secretary, Brian Strutton, said.
"Avoiding strike action and agreeing a deal with their pilots surely must be the desired outcome for British Airways."
British Airways has said the strike action was unjustifiable as its pay offer was fair and that the strikes would destroy the travel plans of tens of thousands of customers.
The airline said in August it was exploring options to supplement its fleet with aircraft and crew from other airlines, a practice known as wet-leasing, and working with partner airlines to schedule larger aircraft to take more customers.
"BALPA has cynically waited until we have helped the vast majority of customers with alternative travel arrangements, and our planning for a strike has reached a critical stage," British Airways said.
"Our customers need the certainty that BALPA will call off the strikes for good, not just for two days next week.