* Lisbon agrees 4.9 bln BES bailout after weekend talks
* Portuguese yields fall, peripheral peers follow
* Fitch says bailout could erode buffer for future shocks
* Greek bonds suffer after Juncker plays down write-off (Adds fresh quotes, prices, Greek bond move)
By Emelia Sithole-Matarise and John Geddie
LONDON, Aug 4 (Reuters) - Portuguese bond yields fell on Monday after Lisbon agreed a near 5 billion euro ($6.6 billion) bailout of its biggest bank in a plan that reassured debt investors there would be no wider strain on public finances.
After frenzied weekend discussions between Portuguese and European Union officials, Lisbon agreed to rescue Banco Espirito Santo, just months after the country exited an international bailout.
Portugal's central bank, which only days ago said that BES could be recapitalized by private investors, said the plan would involve no cost to the public purse because the loan would be temporary and use a chunk of the 6.4 billion euros left from a fund earmarked for banks as part of its EU/IMF bailout.
Portuguese 10-year bond yields dropped 7 basis points (bps) to 3.65 percent, reversing some of the losses from last week when yields rose 20 bps to hit a high of 3.78 percent.
"It is much more of a relief for the peripheral government trade. Now the picture is much clearer and the fiscal position of the Portuguese government will not be compromised," said Nikolaos Panigirtzoglou, a strategist at JP Morgan.
Though many in the market view BES as an isolated case in Portugal, some strategists were concerned that its rescue could diminish the country's bank recapitalisation fund if another bank were to need help.
Ratings agency Fitch said on Monday the split of BES into a "good" and "bad" bank had limited direct fiscal impact on the Portuguese sovereign, but eroded the cash buffer available to deal with any future shocks.
Spanish and Italian bond yields followed Portugal's lower as strategists saw little risk of the contagion that unsettled markets in early July when the BES troubles first came up. Ten-year yields dipped 5 bps to 2.50 percent and 2.70 percent, respectively.
The European Central Bank's ultra-easy monetary policy, which it is expected to reiterate at its meeting on Thursday, and fresh injections of cheap four-year loans later this year are supporting demand for peripheral euro zone bonds.
"We still see an outperformance of peripherals against core (euro zone bonds) from here," said Citi's global head of rates strategy, Alessandro Giansanti.
"Demand, especially for Spain, is really strong. We still see spread tightening, another 15-20 basis points in terms of Spanish outperformance perhaps versus Italy."
Greek bonds underperformed their euro zone government peers on Monday, despite Moody's upgrading of the country's rating by two notches to Caa1 late on Friday citing its improved fiscal position.
Ten-year yields initially dipped in early trading, but swiftly reversed those gains around lunchtime.
The move came shortly after incoming European Commission President Jean-Claude Juncker played down the option of an outright writing-off of part of the euro zone loans to Greece to make the country's debt more manageable.
Traders said the sell-off came amid light trading volumes, which was likely to have exacerbated the move.
By 1500GMT Greek 10-year yields were 7 bps higher on the day at 6.17 percent, some 12 bps above the day's low. (Editing by Gareth Jones)