* 30-year bond yields rise as risk appetite fights back
* But demand for bonds still strong
* German Bund yield remains close to record low (Updates prices, adds detail on Italy)
LONDON, June 11 (Reuters) - Euro zone government bonds were lifted from multi-year lows on Tuesday, as a pickup in risk sentiment globally appeared to put a dent in a stellar fixed income rally.
Thirty-year bond yields in Germany and France rose 4-5 basis points each in a second straight day of sharp rises. .
Worries about a bitter trade war and recession risks have pushed investors into even longer-dated bonds in recent weeks.
But a U.S. decision to hold off from imposing import tariffs on Mexico at the end of last week has brought some relief to world markets, lifting stocks.
Speculation about U.S. rate cuts has also bolstered sentiment in stock markets.
France's 30-year bond yield was trading at 1.1%, almost six bps above more than 2-1/2 year lows hit last week.
"It clearly points towards very lop-sided positioning that is being washed out," said Christoph Rieger, head of rates and credit research at Commerzbank, referring to the rise in longer-dated bond yields.
"And that started yesterday where a correction was triggered by modest risk on."
European stocks were broadly firm while U.S. stocks opened higher, edging back towards record territory. The Dow Jones Industrial Average rose 0.45%.
Still, analysts viewed the move in bonds as a "correction" rather than a change in trend for a market that has seen huge fund inflows this year as investors brace for an increasingly bitter trade war and its repercussions for the world economy.
And some 10-year euro zone bond yields edged lower, keeping recent lows within sight, in a sign that investor pessimism remains entrenched.
U.S. President Donald Trump said on Monday he was ready to impose another round of punitive tariffs on Chinese imports if he cannot make progress in trade talks with China's president at a Group of 20 summit later this month.
Germany's 10-year bond yield dipped to minus 0.23% - holding near last week's record lows. Dutch 10-year bond yields remained in negative territory.
"You have to be long globally on fixed income," said Said Haidar, chief investment officer at Haidar Capital. "That move is not done yet. The global data just keeps on going down."
Meanwhile Italian government bond yields fell across the curve despite comments from European Commission president Jean-Claude Juncker that Italy was "moving in an unsound direction" and risked getting into the EU's so-called excessive deficit procedure.
Italy's 10-year government bond yield was heading back down towards its lowest level in a year, and was at 2.311% .
(Reporting by Dhara Ranasinghe; Editing by Catherine Evans, Susan Fenton and Toby Davis)