* German Bund yields stay in sight of 2-1/2 year lows
* Set for third straight week of falls
* British PM May announces June 7 date for departure
* Euro zone periphery govt bond yields tmsnrt.rs/2ii2Bqr (Adds details, updates prices)
By Dhara Ranasinghe and Tommy Wilkes
LONDON, May 24 (Reuters) - Government bond yields in much of the euro zone held near recent 2-1/2 year lows on Friday, as demand for safe-haven debt held strong in the face of concerns about economic growth, trade tensions and more political turmoil in Britain.
British Prime Minister Theresa May announced she would step down as Conservative Party leader on June 7, paving the way for a new leader who could pursue a more decisive split with the European Union. May’s departure also raises the chances of an unpredictable snap election.
This comes in a week that has seen more disappointing economic data and growing fears that a U.S.-China trade spat could become a more entrenched strategic dispute between the world’s two largest economies.
“The general assumption in the market up until now was that things would get better,” said Peter Schaffrik, global macro strategist at RBC Capital Markets in London.
“But then the U.S.-China trade talks broke down, Brexit uncertainty is rising and the data is not improving. If you put that altogether it is positive for bonds.”
Ten-year bond yields in the United States, Germany, Japan and Britain were all set for a third straight week of falls.
Germany’s 10-year bund yield was marginally higher at minus 0.11%, just 2 basis points away from recent 2-1/2 year lows.
Those lows have prompted several banks to slash their German bond yield forecasts, reversing earlier predictions for a rise in yields by year-end.
France’s 10-year bond yield was steady at 0.28%, within striking distance of 2-1/2 year lows, while 10-year Austrian and Belgium bond yields fell 3 bps apiece .
“To be really bearish on Bund yields you need to expect the ECB to announce a balance sheet reduction and that’s not going to happen for a few years,” said Eric Oynoyan, G10 senior interest rate strategist at BNP Paribas.
The European Central Bank ended its asset purchase scheme at the end of last year but it reinvests funds from maturing bonds, keeping bond yields down.
U.S. Treasury yields were higher on Friday after falling to their lowest levels since 2017 on Thursday.
The yield curve as measured by the gap between three-month and 10-year Treasury yields has inverted, however, a sign that investors are worried about the economic outlook.
Italian bond yields tumbled to 2-1/2 week lows, with 10-year yields touching 2.55% after conciliatory comments from Italy’s deputy prime minister, Matteo Salvini, about Rome’s spending plans.
Two and five-year Italian yields dropped around 10 bps, putting them on track for their biggest daily fall since March.
Salvini said that his League party wanted to change EU fiscal rules to push through tax cuts because doing so under current rules would cause the deficit to overshoot and lift debt costs, something he does not want to do.
Salvini added he was ready to discuss the issue with French and German leaders, in remarks that contrasted with recent comments that he was ready to rip up EU budget rules.
“The market is desperate to hang on to any positive news on Italy,” said Rabobank rates strategist Lyn Graham-Taylor.
“Everyone wants to go long Italy unless told otherwise.”
Editing by Catherine Evans and Alison Williams