* German 10-year yield falls to 5-wk low of -0.04 pct
* EC says EZ growth at 1.2 pct, from 1.3 pct in Feb
* Italy's debt to grow as economy slows, EC says
* Italy/Germany bond yield gap widens to 263 bps (Updates prices, adds detail on Italy)
By Virginia Furness
LONDON, May 7 (Reuters) - German government bond yields hit five-week lows on Tuesday and Italian shares fell, led by the country's banking index, after the European Commission revised down euro area growth forecasts and cut its already gloomy outlook for Italy.
The euro zone economy will rebound next year from a slow-down in 2019 and unemployment will fall further, but inflation is likely to stay at this year's levels and below the European Central Bank's target, the European Commission said on Tuesday.
It forecast domestic euro zone growth of 1.2 percent this year, slower than the 1.3 percent it predicted in February.
The report prompted further buying of German government bonds -- after an apparent deterioration in Sino-U.S. trade relations led investors to buy safe haven assets on Monday -- and pushed yields down to a five-week low of -0.04 percent .
Other bond yields in the bloc were also around three basis points lower.
The fall in rates sets a good tone for Ireland's 2050 syndication later this week. Irish 10-year government bond yields fell to 0.51 percent, their lowest since December 2017, while Ireland's 30-year benchmark touched a three week low of 1.33 percent,.
The report also renewed investor focus on Italy's economic outlook, particularly its budget deficit. Italy was set on a collision course with the EU over its spending plans last year, prompting investors to sell its government bonds, but Rome made a last-minute concession to abide by EU rules.
The Commission also cut Italy's growth forecast to 0.1 percent, down from 0.2 percent, and said the country's deficit could widen further beyond the 3 percent ceiling set by the European Union.
Italian 10-year government bond yields hit a day's high of 2.6 percent, before pulling back to 2.59 percent.
While the reaction in Italian bonds was muted, the Germany/Italy bond yield spread reached its widest since April 26 at 263 basis points.
"The Italy spread did widen on the release of the forecast but there's been a mini-recovery," said Peter Chatwell, a strategist at Mizuho in London. "The EU don't seem to be telling us anything we don't know, but the market is using that as a catalyst to re-price."
Italian shares fell into negative territory, with the banking index 1.7 percent lower at 1208 GMT as investors focussed on the deficit forecast.
With no changes in the government's spending policies, Italy's deficit is set to grow to 2.5 percent of output this year and climb to 3.5 percent in 2020, beyond the 3.0 percent ceiling set by EU fiscal rules, the EC said.
"Clearly that is way beyond what will be deemed acceptable and that has seen the underperformance of Italy," said Richard McGuire, head of rates strategy at Rabobank.
Economy minister Giovanni Tria shrugged off the EU forecasts, saying they reflected the government's own outlook and were "more political than economic" as they did not consider government commitments in its 2020 budget to cut the deficit. (Reporting by Virginia Furness and Josephine Mason; editing by Kirsten Donovan and Gareth Jones)