British Airways and its pilots have been urged by Number 10 to "sort out" the dispute which will see pilots walk out next week in a row over pay.
"The unions and BA need to get round the table and sort this out. The public would expect nothing less," it said.
BA pilots are due to strike on Monday and Tuesday over a pay offer pilots' union Balpa says is too low.
The vast majority of flights are expected to be cancelled on those two days, causing knock-on disruption.
BA would not say how many flights had been affected, but reports suggested it was around 1,600 flights.
"Nobody should have their travel plans disrupted or their holidays ruined," Number 10 said.
The airline says it has emailed customers travelling on flights that are affected but the flight's status can still be checked on the website.
The airline and the union did not provide an update on the status of their dispute on Friday.
The two-day strike, set for next week, follows failed negotiations between the union and the airline over a pay offer of 11.5% over three years.
Unite and GMB, representing cabin crew and engineers, have accepted the offer.
However, pilots have argued that the pay award should be higher, following recent years of low pay increases and BA's recent strong financial performance.
BA has said it was open to "constructive talks", but said Balpa was not acting in good faith.
The union has said it would call off the strike if BA would discuss a new proposal outlined in a letter on Thursday to the airline.
The union's general secretary Brian Strutton said his members were still "very angry" with BA, but were also willing to be flexible.
"They also want to leave no stone unturned in trying to find a resolution to their dispute," he said.
In response, BA had said: "We do not believe the union is acting in good faith by making an 11th-hour inflated proposal which would cost an additional £50m."
The airline said Balpa should return to the talks without pre-conditions. The union was acting "cynically" by waiting until a late stage when the airline had already made arrangements to manage the industrial action, BA added.
"Our customers need the certainty that Balpa will call off the strikes for good, not just for two days next week," the airline said.
A further day of strike action is scheduled for 27 September.