* Italian yields set for biggest weekly fall since June 2018
* Italy best performing major bond market this week
* ECB easing speculation, budget news boost Italian BTPs
* U.S. jobs data awaited
* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Updates throughout with analysis, charts, comment)
LONDON, July 5 (Reuters) - Italy has joined a huge rally in world bond markets, with yields set on Friday for their biggest weekly fall in more than a year as Rome avoided a clash with the European Union over its fiscal policy for now and hopes for monetary easing soon grow.
While bond yields across the euro area this week hit fresh milestones, Italy delivered eye-popping moves of its own with 10-year borrowing costs falling to their lowest since 2016.
Italy on Wednesday dodged the threat of EU disciplinary action over its public finances after persuading the European Commission that new measures submitted would help bring its growing debt into line with EU fiscal rules.
Speculation that the ECB could deliver not only interest-rate cuts but possibly a fresh round of monetary stimulus were fuelled this week by ECB officials, pushing euro zone bond yields down further.
Investors are also betting that France's Christine Lagarde, picked by EU leaders this week to be next ECB chief, will double down on a dovish monetary policy stance.
"The ECB plays a considerable role for the move in Italian bonds this week, but also there's the fact that we've had some positive headlines on the budget deficit," said Ross Hutchison, a fund manager at Aberdeen Standard Investments.
With more than half of the of the euro zone government bond universe in negative yield territory, investors piled into positive-yielding Italian bonds, known as BTPs.
Italy's 10-year bond yield, down a basis point on Friday at 1.66%, has slid around 45 basis points this week -- set for its biggest weekly decline since June 2018.
That slide is more than double the falls seen in other major government bond yields.
Interactive version of this chart: https://tmsnrt.rs/2FV7gca
The euro zone's economic slowdown is no longer temporary, and the ECB needs to provide more stimulus to fulfil its mandate, Governing Council member Olli Rehn told German newspaper Boersen Zeitung.
"For now, the markets are reacting to expectations of ECB quantitative easing and Italy has always been one of the main beneficiaries of that," said Mohammed Kazmi, portfolio manager for UBP in Geneva.
Two-year Italian bond yields, steady on Friday at 0.06%, briefly turned negative earlier in the week.
The closely-watched Italian/German 10-year bond yield gap is hovering around 200 bps, near its tightest in over a year . "Spread levels below 200 bps look hardly sustainable beyond the medium term," said Benjamin Schroeder, senior rates strategist at ING. "Eventually, we think the current government will clash with the EU over the 2020 budget in autumn at the latest."
Most 10-year bond yields in the bloc inched higher but trade was subdued ahead of key U.S. jobs data later. Germany's 10-year bond yield was at minus 0.39%, having dropped below the ECB's minus 0.40% deposit rate on Thursday for the first time.
Greek yields edged up before elections this weekend. Opinion polls suggest the opposition conservatives are likely to ride a wave of anger over continuing austerity measures and seize power.
(Reporting by Dhara Ranasinghe; Editing by Catherine Evans and Alexander Smith)