* Union says will start Germany-wide strikes on Fri
* Cabin crew on strike in Frankfurt, Berlin, Munich on Tues
* Over 300 flights cancelled
* Workers want 5 pct pay increase, outsourcing guarantees (Recasts with union on fresh strikes)
By Peter Maushagen and Victoria Bryan
FRANKFURT, Sept 4 Lufthansa cabin crew will strike throughout Germany on Friday for a full 24 hours, upping the stakes in a row over pay and conditions that threatens to drag on for weeks and cost Germany's biggest airline tens of millions of euros.
Cabin crews walked out at Frankfurt, Munich and Berlin airports on Tuesday, forcing Lufthansa to cancel hundreds more flights following strike action on Friday that left 26,000 passengers stranded.
The UFO union said a Germany-wide strike would run from 0000-2400 CET (2200-2200 GMT) on Friday and union head Nicoley Baublies, speaking to a German broadcaster, called on Lufthansa to start mediation, a process that would halt the strikes.
Lufthansa repeated its earlier statement that it saw no reason for mediation. "The offer already made is reason enough to return to the negotiating table," a spokesman said.
Lufthansa, which operates from 16 airports in Germany, cancelled over 300 flights, or more than one in six of its daily total, on Tuesday.
"It is difficult for the company to cushion the impact. We cannot just get new flight attendants and the personnel buffer is limited," Lufthansa spokesman Klaus Walther said.
Its Austrian Airlines unit, unaffected by the strikes because its staff are on separate contracts, said it was using larger aircraft on routes to Germany to help out its parent.
While Germany has a track record of mostly harmonious labour relations compared with other major European countries such as France, its airlines and airports have been hit by a string of disputes in recent years as companies battle to cut costs to cope with the rise of low-cost carriers, soaring fuel prices, fast-growing Middle East airlines and an air travel tax.
A strike by Lufthansa pilots in 2010 caused more than 2,800 flight cancellations, and earlier this year a strike by airfield staff at Frankfurt airport also hit Lufthansa's business.
U.S. soldier Ron Smith, travelling home to Denver, said it seemed each time he flew through Frankfurt he ended up getting stranded. "This wouldn't happen in the U.S.," he complained.
Trade union UFO, which represents around two thirds of Lufthansa's 18,000 cabin crew, had called for eight hours of strikes in Frankfurt and Berlin and 11 hours in Munich on Tuesday.
Talks between Lufthansa and UFO broke down a week ago, having failed to result in an agreement for 13 months, and have so far not resumed, with both sides adamant the other should make concessions first.
The union wants a 5 percent pay increase and guarantees against outsourcing and the use of temporary workers.
Lufthansa, which is slashing costs in a bid to boost its earnings by 1.5 billion euros ($1.9 billion), has offered a pay increase of 3.5 percent in exchange for longer hours.
UFO head Baublies had threatened the next step could be full-day walkouts by Lufthansa cabin crew across Germany. He has previously said the union was prepared to strike into the autumn or winter.
Analysts have estimated the strikes so far could cost about between 5 million euros and 10 million a day, but Equinet analyst Jochen Rothenbacher warned that sum could jump to as much as 50 million if full-day strikes across Germany shut down all flights.
Lufthansa's Walther said the airline was mulling legal steps against the union.
At its main hub in Frankfurt alone, Lufthansa scrapped around 217 flights on Tuesday, with about half of short- and medium-haul flights affected, but also one-third of its more lucrative long-haul flights.
The airline, which normally operates about 1,800 flights a day around the world, also cancelled half of long-haul trips due to depart Munich and expects to cancel about a quarter of short-and medium-haul flights.
Lufthansa had sent 18,000 text messages to customers' mobile phones by this morning to inform them of flight cancellations and delays, and it was supplying stranded passengers at airports wi t h drinks and snacks.
Lufthansa shares, which have fallen 17 percent over the past year, closed down 1.3 percent at 9.659 euros.
($1 = 0.7947 euros) (Writing by Harro ten Wolde and Maria Sheahan; Editing by Mark Potter and David Holmes)