* U.S. bonds underperform as June Fed rate hike expected
* U.S./UK spread at highest in 34 years as UK economy struggles
* Italian yields edge up further on early election jitters
* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Adds background, updates prices)
LONDON, May 1 (Reuters) - The gap between U.S. and German 10-year benchmark bond yields was a shade off its widest level in nearly three decades on Tuesday as the economic and monetary policy outlooks of the United States and euro zone start to take different paths.
In thin trading on Tuesday with much of Europe on May Day holiday, U.S. 10-year Treasury yields rose above 2.977 percent, extending the gap over their German counterpart.
The dollar was at its strongest against a basket of currencies since early January on increased expectations that the U.S. Federal Reserve will raise interest rates three more times this year to add to the one increase already made in 2018.
The central bank is expected to hold U.S. rates steady this week but is likely to encourage expectations further that it will increase them in June due to rising inflation and low unemployment. The Federal Open Market Committee (FOMC) is due to announce its decision at 2 p.m. EDT (1800 GMT) on Wednesday.
Core euro zone bonds have picked up demand in recent days since a European Central Bank meeting on expectations that policymakers will adopt a relatively cautious stance.
"Higher U.S. core PCE inflation and Wednesday's FOMC meeting should pave the way for a June hike (from the Fed)," Commerzbank analysts said in a note. However, subdued inflation on the other side of the Atlantic, along with redemptions and other technical factors, should stabilise European government bonds, they added.
The gap between 10-year German and U.S. bond yields was at 240 basis points, less than a basis point off the widest level since March 1989 touched last week.
Though this spread does not account for the different valuations of the currencies of either region, it still indicates how differently investors view the two regions in terms of how far central banks have to go in removing post-crisis stimulus.
The ECB still buys 30 billion euros of bonds a month as part of its stimulus programme and rate hikes are still far away by investors' reckoning, whereas the Fed is already running down its quantitative easing scheme.
In addition, the gap between British and U.S. 10-year government bond yields hit its widest since 1984 on Tuesday, reflecting sharp shifts in interest rate expectations in the two countries in recent days.
Most euro zone bonds were roughly unchanged on the day, Italian yields rose a touch, having jumped 3-5 basis points across the curve on Monday on political jitters.
On Tuesday, the Italy/Germany 10-year bond yield spread reached its widest in two weeks at 122 basis points following Monday's headlines that raised the possibility of an early election.
5-Star leader Luigi Di Maio called for new elections in June, saying efforts to form a coalition after March's inconclusive vote had gone nowhere.
Elsewhere, Greek government bond yields stuck to the 2-1/2 months lows hit after OECD chief Angel Gurria said on Monday that Athens has made enormous reform efforts since its debt crisis broke out and deserved debt relief.
(Reporting by Abhinav Ramnarayan, additional reporting by Fanny Potkin. Editing by Mark Heinrich and David Stamp)