* Italy's 2yr yield down 80 bps
* Polls show most Italians want to stay in euro
* Euro zone inflation beats forecasts
* Euro zone bond markets in May: tmsnrt.rs/2xvCNQb (Updates prices, developments in Italy, Spain)
By Dhara Ranasinghe and Abhinav Ramnarayan
LONDON, May 31 (Reuters) - Italy's borrowing costs fell sharply for a second day on Thursday as news that one of Japan's largest institutional investors is looking to buy short-dated Italian debt helped stabilise a market battered by a political crisis in Rome.
Japan Post Insurance Co's chief investment officer told Reuters the firm, also known as Kampo, is looking to buy short-term Italian government bonds after the recent sell-off made them inexpensive.
With over $700 billion of assets, Kampo is one of the biggest Japanese investors.
On Tuesday, Italy's 2-year bond yields posted their biggest one-day jump in 26 years on fears that fresh elections in the euro zone's third biggest economy could strengthen the hand of anti-establishment parties.
But the past two days have seen some stability thanks in part to renewed efforts to form a government and avoid new elections.
In addition, two polls showing that most Italians want to stay in the euro allayed some fears of anti-euro sentiment taking hold in Italy.
"For a macro investor, one who is not constrained by mark to market issues, buying short-dated debt here or looking at markets from a fundamental perspective and not paying too much attention to headline risk or short-term price action, is sensible," said Peter Chatwell, head of rates strategy at Mizuho in London.
Italy's 2-year bond yield was down 73 basis points in late trade at 1.26 percent on Thursday, comfortably below 5-year highs touched this week at around 2.7 percent.
Japanese investors are big buyers of euro zone bonds and their activity is closely watched. They bought a record $2.57 billion worth of Spanish bonds in March.
Italy's 10-year bond yield was down 21 bps at 2.84 percent, while the Italy/Germany 10-year bond yield spread tightened to 250 bps from 293 bps late on Wednesday.
Still, that spread has increased more than 100 basis points this month - the biggest monthly spread widening since 2011.
Italian five-year credit default swaps fell 19 basis points from Wednesday's close to 233 bps, according to data from IHS Markit.
"The two-year (yield) move was obviously greatly exaggerated and all were pricing an inversion of the yield curve and thinking this will end very badly," said Carl Hammer, head of global macro and FX research at SEB in Stockholm.
"We don't anticipate a crisis in Italy but there will be more worries so it will be a factor for investors to consider until they get some clarification."
There was some focus on Spain, where Prime Minister Mariano Rajoy's hours in office appeared numbered after reports that a Basque political party would back a no-confidence vote over a corruption case.
Still, Spain's 10-year bond yield was down 10 bps at 1.51 percent as the rebound in Italian bonds supported peripheral bond markets.
Yields on top-rated euro zone bonds were also lower in late European trade, reversing earlier rises, after a sharp fall in Deutsche Bank shares and renewed concerns about a trade war re-ignited demand for safe-haven bonds.
Germany's 10-year bond yield was down 1.5 bps at 0.33 percent, but remained well above a 13-month low hit on Tuesday at 0.19 percent.
Data showing inflation in the euro area rose to 1.9 percent in May from 1.2 percent in April, well above expectations, had pressured most bond markets earlier on.
Reporting by Dhara Ranasinghe and Abhinav Ramnarayan; Additional reporting by Claire Milhench and Sujata Rao Editing by Mark Heinrich and Richard Balmforth