By Kate Abnett

BRUSSELS (Reuters) -The European Union's agriculture sector loses an average of 28.3 billion euros ($31.9 billion) each year from extreme weather made worse by climate change, EU-backed analysis published on Tuesday showed.

Most of these losses - which are equivalent to 6% of annual EU crop and livestock production - are not insured. Just 20-30% of farmers' climate-linked losses were covered by public, private or mutual insurance systems, said the report, backed by the European Commission and European Investment Bank, and produced by insurance broker Howden.

"We need to do something to cover the remaining losses," EU agriculture commissioner Christophe Hansen said. He urged countries to use their EU farming subsidies to address climate risks.

Europe's farming industry is both hit hard by climate change impacts like drought and extreme rainfall, and itself putting intense pressure on the environment - through planet-heating methane emissions, pollution from fertilisers and industrial-scale use of water.

At the same time, influential agriculture lobby groups have taken aim at Europe's green agenda, staging months of protests last year seeking a weakening of environmental policies.

The European Commission announced plans last week to soften some environmental conditions on EU farming subsidies, while also proposing rules to speed up emergency funding for farmers hit by natural disasters.

Farmers' average crop losses are expected to increase by up to 66% by 2050 without stronger action to address climate change, the analysis said. Currently, drought causes more than half of total agricultural losses.

With southern Europe hit particularly hard by drought, the analysis said that by 2050, in a "catastrophic" year, annual losses in Spain and Italy alone could hit 20 billion euros.

The European Investment Bank, the EU's lending arm, said the analysis would guide its efforts to support farmers, which include financing investments like irrigation, and providing loans and guarantees.

The EIB also plans to increase its spending on water projects - a move that could benefit farmers - according to a leaked draft of a European Commission water strategy, reported by Reuters last week.

An EIB spokesperson did not immediately respond to a request for comment on this funding.

($1 = 0.8877 euros)

(Reporting by Kate Abnett. Editing by Mark Potter)