* Demand soars for Portugal as country wins back investment rating
* Borrowing costs converge with peers for first time in years
* Portugal-Italy yield spread tightest since March 2010 at 33 bps
* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Rewrites top, updates prices)
LONDON, Sept 19 (Reuters) - The gap between Portuguese and Italian 10-year government bond yields narrowed on Tuesday to levels not seen since the start of the euro zone debt crisis of 2010-2012, showing how much investor sentiment towards Portugal has improved this year.
As one of the only junk-rated euro zone countries, Portugal has traditionally had much higher borrowing costs than its larger and better-rated southern European peers.
However, a strong rally in Portuguese debt over the last two sessions has accelerated a trend seen in recent months: the country is now catching up with Italy and Spain in the eyes of investors.
"It reflects the narrowing ratings differential and the fact that some political risk premium is still baked into Italian government bonds," said ING strategist Martin van Vliet.
Portugal's bond market received a huge boost when S&P Global became the first major ratings agency to give the country back an investment grade rating on Friday, more than five years after it first sank into junk territory.
Portugal's 10-year government bond yield spread over Italy narrowed to around 34 basis points, the lowest since March 2010. At the start of the year, that difference was as high as 211 basis points.
The spread over top-rated Germany was also close to its narrowest level since December 2016 at 198 bps.
That spread tightening reflects improved sentiment towards Portugal, which was hit last year by fears it could loose its investment grade rating with smaller ratings agency DBRS that it needed to stay in the European Central Bank's bond-buying scheme.
Portugal's 10-year bond yield was down 5 basis points at 2.44 percent on Tuesday, continuing to outperform euro zone peers.
Van Vliet said Portugal's recovery from the euro zone debt crisis - when it needed a bailout from European authorities - is strong, but cautioned that it is still a weaker credit than Italy because of its external debt position.
Portugal's outstanding private debt stood at 280 percent of the country's economic output last year, comprising 178 percent for companies and 103 percent for households. <http://reut.rs/2xiwTjp
"I think this rally is on speculation that Portugal could now be included in many benchmark indices," Van Vliet said.
Many large bond indexes provided by investment banks only include investment grade borrowers, and inclusion in these usually guarantees a new influx of investors and lower yields.
However, many index providers require an investment grade rating from at least two of the three main credit ratings agencies, and Portugal now only has one. It is rated Ba1 by Moody's and BB+ by Fitch.
Most bond yields in the bloc were 1-3 bps lower ahead of a U.S. Federal Reserve meeting, which concludes on Wednesday.
The central bank of the world's biggest economy is expected to provide details on how it will reduce a massive balance sheet run-up through years of post-crisis money printing.
This is seen as significant by European investors as the ECB is also expected to tighten policy, possibly by announcing in October its plans for ending its own money-printing scheme.
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(Reporting by Abhinav Ramnarayan; Additional reporting by Dhara Ranasinghe; Editing by Andrew Heavens)