* Still sees 2013 pretax loss of about 400 mln euros
* Says some sectors improving, but no construction recovery
* Says could see cyclical upturn in prices
* Q3 pretax loss 64.3 mln euros vs Rtrs poll avg 62.3 mln (Recasts with comments on European steel market)
FRANKFURT, Nov 14 (Reuters) - Germany's Salzgitter said on Thursday that any green shoots of economic recovery in Europe were so far eluding the steel sector because of oversupply, reaffirming its full-year outlook for the pretax loss to quadruple.
The $500-billion-a-year global steel industry, a gauge of economic health, has suffered from a drop in demand in Europe and worries over Chinese growth prospects.
Salzgitter, Germany's second-biggest steelmaker, is cutting more than 1,500 jobs, or 6 percent of its workforce, as it battles the downturn in which demand for cars, appliances and new buildings remains weak in austerity-hit Europe.
While some sectors in Europe have recently reported positive developments, Salzgitter said there is no improvement in the construction industry yet.
However, prices could firm up thanks to a slight pick-up in demand and low inventory levels of traders and consumers, even if the chasm between the northern and southern European steel markets is unlikely to narrow in the short term.
For this year Salzgitter expects its group pretax loss to widen to about 400 million euros ($536 million) from 102 million euros last year.
In the third quarter its loss widened to 64.3 million euros from 24.5 million, roughly in line with the consensus forecast in a Reuters poll.
ArcelorMittal, the world's largest steelmaker, said last week that its two-year slump was over and prospects for 2014 are looking up after higher U.S. steel shipments and mining output boosted third-quarter profits.
Germany's top steelmaker ThyssenKrupp is due to publish quarterly results on Nov. 21. ($1 = 0.7460 euros) (Reporting by Maria Sheahan; Editing by David Goodman)