* Southern European debt in demand in "buy the dip" trade
* Italian yields down 5 bps, still up 10 bps for week
* Italy's League says leaving the euro not a priority
* Euro zone periphery govt bond yields tmsnrt.rs/2ii2Bqr (Updates prices)
By Abhinav Ramnarayan
LONDON, May 11 (Reuters) - Investors bought up Italian government bonds on Friday, taking advantage of this week's sharp rise in yields and soothed by some moderate comments from the anti-establishment parties that look likely to form Italy's next government.
Italian 10-year yields were set for their biggest weekly rise since February, although they were down 5 basis points on Friday at 1.88 percent.
Italy's 5-Star Movement and League parties are hoping to reach agreement on forming a coalition agreement in the coming days.
On Friday, a 5-Star Movement source told Reuters the new government will be "rational and reasonable" on public accounts, while a top League senator said abandoning Europe's single currency is not one of the party's priorities.
Those comments address two of the main concerns investors have about a potential coalition between the two parties.
"The League is reported as saying that (leaving the) euro was not one of the priorities, this gives investors confidence to buy the dip," said DZ Bank analyst Pascal Segesser. "Also in general there's a feeling that because of Macron and Merkel, there will be some stability in the region."
Spanish and Portuguese 10-year borrowing costs fell 2-3 basis points each, the three Southern European countries outpacing better-rated peers at the end of a week in which Italian political worries had hurt "peripheral" debt. ,
In addition, one of Italy's problem banks, Monte dei Paschi di Siena, swung to a first-quarter net profit of 188 million euros ($224 million) helped by falling writedowns and cost cutting.
Analysts said an Italian bond sale also went smoothly, boosting sentiment after a turbulent week.
Central bankers around the world also appear to have become even more cautious as concerns over inflation and international trade cloud the global economic picture.
On Thursday, the Bank of England held rates against recent expectations and New Zealand's Reserve Bank said the official cash rate will remain at 1.75 percent for "some time to come".
This leaves the U.S. Federal Reserve as the only major central bank committed to rate hikes, but lower-than-expected inflation in the world's largest economy has put some doubt over the pace of these hikes.
Elsewhere, European Central Bank President Mario Draghi said the euro zone needs a common "fiscal instrument" to hold its member countries together even when they come under attack in financial markets.
Outside of Southern Europe, most euro zone government bond yields were a touch higher. Germany's 10-year Bund yield rose 1 basis point to 0.56 percent. (Reporting by Abhinav Ramnarayan; Additional reporting by Dhara Ranasinghe; Editing by Keith Weir and Hugh Lawson)