* 660 flights cancelled Monday, 603 because of strike
* Strike extended until 0400 GMT Wednesday
* Airlines bus passengers to airports in Dresden, Hanover
* Union says strike may be extended again (Adds cancellations for Tuesday)
BERLIN, March 13 (Reuters) - Berlin's airports will remain paralysed on Tuesday after ground staff extended a strike, stepping up pressure in a dispute over pay that has already caused the cancellation of more than 1,000 flights since Friday.
Ground staff at Berlin's two airports started their latest walkout on Monday morning after a break over the weekend. The trade union Verdi said earlier the strike would be extended until Wednesday morning.
The walkout at Tegel and Schoenefeld airports - which are served by airlines including Air Berlin, Ryanair , easyJet and Lufthansa - led to the cancellation of 660 flights on Monday, virtually all the flights due to use the airports.
The operator of Berlin airport said late on Monday that a further 603 flights would be cancelled on Tuesday. On Friday, 670 flights were cancelled.
Along with the cancellations, airlines are trying to divert passengers. EasyJet said it was operating to Dresden airport; Air Berlin will transfer some passengers to Hanover to catch flights.
Berlin Mayor Michael Mueller was among those whose travel plans were disrupted on Monday, having to fly to Moscow via Dresden instead.
Air Berlin said the strike was costing the industry millions of euros a day, but that it was too early to give an exact figure.
The strike is due to end on Wednesday at 0500 CET (0400 GMT). While ground staff are ready to engage in talks to end the strike if Berlin airports make an improved offer, they could also decide to extend the walkout if no new offer is made.
"It may well be that early tomorrow morning we say we will continue the strike on Wednesday. It's a 50:50 chance," Enrico Ruemker, who heads the strikes for Verdi, told Reuters.
Ground staff, whose roles include check-in, loading and unloading planes and directing aircraft on the tarmac, are employed by companies including WISAG, Aeroground, Ground Solution, AHS and Swissport Berlin.
A spokesman for the employers said the strike was irresponsible. "It won't help solve the row," he said.
The union wants an increase in pay for ground staff to 12 euros ($12.80) an hour from about 11 euros as part of a one-year collective agreement. Management first offered about 10 cents more an hour over four years and then improved that offer to an 8 percent increase over three years. (Reporting by Victoria Bryan, Klaus Lauer and Peter Maushagen; Additional reporting by Edward Taylor; Editing by Larry King)