British Airways' chief executive Rod Eddington said there would be no flights by the airline at London's Heathrow airport until at least 1700 GMT, but did not elaborate on how the strikes by baggage handlers and other ground staff would be overcome.
Other airlines faced knock-on disruption at the world's busiest international airport. Australia's Qantas Airways Ltd, Finnish national carrier Finnair, Sri Lankan Airlines, GB Airlines and British Mediterranean Airlines were affected.
British Airways said about 1000 of its baggage handlers, bus drivers and other staff stopped work on Thursday in support of hundreds of workers sacked this week by a catering firm that provides the airline's in-flight meals.
Unions said check-in staff went home after suffering abuse from angry passengers.
The strike left thousands
stranded at Heathrow airport
"I would like to apologise unreservedly to our customers," Eddington said in a statement. "Nearly 100 of our aircraft and 1000 pilots and cabin crew are in the wrong places."
Eddington called on the Transport and General Workers' Union and managers of the Gate Gourmet UK catering firm to resolve the dispute and "end this misery for our customers".
But negotiations between the two sides ended in failure on Thursday, and it was unclear what would happen next.
British Airways urged people to stay away from Heathrow on Friday and said about 20,000 passengers already stranded should go home or find rooms in packed hotels round the airport.
Hundreds of passengers tried to sleep on the floor at Heathrow's Terminal 4, while many more were left outside after staff closed the doors to prevent overcrowding.
The airline said it had booked a few thousand hotel rooms for passengers.
The chaos was a blow to British Airways, which has been battling against record oil prices, tough competition from low-cost rivals and staff shortages.
The action is in support of sacked
British Airways suffered unofficial strikes in mid-2003 in a dispute over working conditions and narrowly fended off strikes last year after securing a pay deal with ground staff.
As the chaos grew on Thursday, airline staff handed out free bottles of water to passengers on a hot summer's day, and engineers erected large marquees on Terminal 4's forecourt so
people would have somewhere to shelter.
"There is every indication that it is going to get worse before it gets better," said Ian Thompson, 51, due to fly to Los Angeles with his wife Carol, 49. "At the moment we have no idea when we might get away."
In New York, British Airways spokesman John Lampl said passengers were being rescheduled or placed on flights operated by other carriers.
Friday's flights were all cancelled until 1700 GMT. "We will have to wait and see what is going to happen," said Lampl.
The chaos was triggered by a long-running industrial dispute between the Transport and General Workers' Union and Gate Gourmet UK, part of a global group with headquarters in Zurich and Reston, Virginia.
The airline is struggling with
competition and high oil prices
Unions said Gate Gourmet staff walked out in protest at planned changes to pay and conditions. The company said its proposed reforms were needed to safeguard its future.
"If we don't change, the company will not survive," Gate Gourmet's managing director Eric Born said in a statement.
He said the company had not made a profit since 2000 and would lose 25 million pounds sterling ($45.09 million) this year without restructuring.
British Airways shares closed down 1.3% at 292.25 pence on Thursday.