* Spain, Saxony inflation data pushes yields lower
* ECB wary of making new change to policy message - report
* German Bund yields at 3-week low
* Euro zone periphery govt bond yields tmsnrt.rs/2ii2Bqr
By Dhara Ranasinghe
LONDON, March 30 (Reuters) - Most euro zone bond yields fell to multi-week lows on Thursday, as softer-than-expected inflation data from Spain and the German state of Saxony helped dampen speculation that an eventual unwinding of ECB stimulus could come sooner rather than later.
Bond yields across the bloc fell sharply on Wednesday after a Reuters report that European Central Bank officials are wary of making any new change to their policy message in April after small tweaks this month unsettled markets.
That fall gathered momentum on Thursday after data from Spain, the euro zone's fourth biggest economy, showed consumer prices rose 2.1 percent year-on-year in March, compared with a Reuters poll forecast of 2.7 percent.
Inflation in the German state of Saxony rose 1.8 percent year-on-year in March, versus a 2.4 percent rise in February.
"We we've had a weak inflation print from Spain and the Saxony number was slightly lower than we had anticipated," said Rabobank fixed income strategist Lyn Graham-Taylor. "It comes off the ECB article yesterday, which all adds up to a bid for bonds."
Germany's benchmark 10-year government bonds yield fell 2 basis points to a three-week low of 0.33 percent.
Dutch 10-year bond yields also fell to a three-week low , while French yields hit a four-week low at 0.91 percent.
Spanish yield briefly dipped to a one-month low at 1.62 percent, while other euro zone yields were all a touch lower on the day.
Bond yields had opened a slightly higher - a move analysts attributed to overnight comments from two U.S. Federal Reserve officials raising the prospect of a pick up in the pace of interest-rate hikes in the world's biggest economy.
But those moves proved short-lived as focus turned back to the ECB policy outlook.
Speculation about an eventual unwinding of the ECB's ultra-loose monetary policy had gathered pace in recent weeks. At its March meeting, ECB President Mario Draghi said its sense of urgency was over and some policymakers had raised the prospect of a rate rise before quantitative easing ends.
But according to Wednesday's source-based report, one official said the ECB had been overinterpreted by markets at its March 9 meeting.
"My take is that the ECB concluded that enough is enough and stepped up its verbal intervention campaign to play down the speculation," said Martin van Vliet, senior rates strategist at ING.
Money market rates suggest roughly a 50 percent chance of an ECB rate rise in December. That is down from 70 percent earlier this week.
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Reporting by Dhara Ranasinghe; Editing by Alison Williams