Marston said the job losses and part-time work will be accomplished voluntarily.
He said BA, which expects to see a "significant loss'' for the second year running, needed to make changes in order to secure its future in an airline market which is likely to remain tough for some time to come.
"Without changes, we will lose more money with every month that passes,'' a company statement said.
"It is essential we make ourselves more efficient if we are to ensure our long-term survival.''
Marston said the changes would not affect customers, but Pauline Doyle, the UNITE union spokeswoman said the change was worrying.
"They're going to try to get more and more out of fewer and fewer people for less and less money,'' she said.
BA is also planning a freeze on basic pay and said cabin crews operating out of London's Heathrow Airport would be reduced so that the typical 747 jet flying from Heathrow on a long-haul trip would take off carrying 14 members of crew instead of the usual 15.
The changes would take place from the end of November after 1,000 cabin crew said they would take voluntary redundancy and a further 3,000 opted to switch to part-time working.
The economic downturn has hit carriers like BA particularly hard, reporting a record £595m loss in the last year, its worst result in two decades.
The slump, due to fuel costs and low demand, came a year after the company reported a record profit of $1.13bn.