LONDON, Nov 3 (Reuters) - Battered euro zone bond markets fought back on Wednesday, with sovereign borrowing costs down sharply for a second straight session as investors scaled back their most aggressive bets for interest rates hikes in the coming year. European Central Bank chief Christine Lagarde said a rate rise next year was "very unlikely" as inflation remains too low, also prompting a key market gauge of long-term euro zone inflation expectations to retreat further from recent highs above 2% . read more Disappointment that Lagarde did not push back more firmly against hefty market pricing of rate hikes after last Thursday"s ECB meeting had triggered a fresh sell-off in bond markets that sent borrowing costs to multi-month highs. But a calmer tone has emerged with the latest ECB talk and this week"s Australian central bank meeting bringing some restraint to investors" more aggressive thinking on the rate outlook for major economies. The Reserve Bank of Australia took a major step on Tuesday towards unwinding extraordinary pandemic stimulus, but pledged patience and rejected market talk of an early rate hike. read more European money markets now price in one 10-basis-point rate hike by December 2022. At the start of the week, market pricing had pointed to a 10-bps move by July 2022, and two hikes by October, indicating a tightening in monetary policy that was well out of sync with the ECB"s policy guidance. As rate-hike bets eased, so too did sovereign borrowing costs. Germany"s 10-year Bund yield fell to a one-month low at -0.19% , below roughly 2-1/2 year highs hit last week at -0.064% . And 30-year Bund yields fell to a two-month low at around 0.12% . "As the dust settles, there"s a clearer look at whether the ECB will hike next year, and markets are coming to the realisation that even if inflation rises above target next year, they (the ECB) might not act so fast," said DZ Bank rates strategist Rene Albrecht. "I think the market is realising that it was getting ahead of itself and the positioning is cleaner." Bond markets have become more volatile recently, with yields swinging sharply as investors try to assess the outlook for inflation and ECB policy. Having shot up last week, Italian 10-year bond yields, for instance, fell 13 basis points on Tuesday in their biggest one-day fall since May 2020. They fell a further 5 bps on Wednesday to 1.05% , having touched more than one-year highs near 1.29% on Monday. "We are having this massive to and fro on policy expectations and that will probably continue as we have the Fed this evening and the BoE (Bank of England) tomorrow," said Rabobank senior rates strategist Lyn Graham-Taylor. The U.S. Federal Reserve is expected to conclude a two-day meeting on Wednesday with a decision to taper its $120 billion-a-month asset purchase programme by around $15 billion a month. read more Reporting by Dhara Ranasinghe; Editing by Kim Coghill, Mark Heinrich, Nick Macfie, William Maclean