Euro zone bond yields steadied on Tuesday after a recent run of declines, as investors awaited U.S. inflation data that could offer hints on the Federal Reserve's rate-cutting path and the European Central Bank's (ECB) policy decision later this week.

The German 10-year bond yield, the benchmark for the euro zone bloc, was little changed at 2.17%. It touched a one-month low of 2.147% on Friday.

Meanwhile, Germany's two-year bond yield, which is more sensitive to changes in ECB rate expectations, was flat at 2.217%. The yield also touched a more than one-month low of 2.208% on Monday.

The ECB looks all but certain to cut rates by 25 basis points on Thursday, with investors seeking clues on what action the central bank might take after that.

Traders have fully priced in a cut later this week, and see a 50% chance of another 25 bps cut in December but smaller odds of a move in October. Overall, money markets are pricing in rate cuts of 62 bps from the ECB by the end of the year.

"The overall message is going to be: disinflation is still on track, growth is a bit weaker than expected. But the fact that you've these forecasts that show return to the 2% inflation goal is going to take some time, the underlying message will be caution," said Paul Hollingsworth, chief Europe economist at BNP Paribas.

Hollingsworth expects the ECB cut rates once per quarter until it gets to 2.5%.

Italy's 10-year yield was flat at 3.549%, and the gap between Italian and German bond yields stood at about 137 bps.

A hotly anticipated debate between U.S. presidential candidates Kamala Harris and Donald Trump as well as U.S. inflation data on Wednesday will be among the other main catalysts for markets.

U.S. and euro zone government bond yields have tumbled in recent days after softer-than-expected U.S. economic data raised concerns about a potential recession and prompted traders to price in aggressive rate cuts by the Fed.

The Fed is scheduled to meet next week. Traders are certain that the policymakers will cut rates by 25 bps but are debating the possibility of a bigger 50 bps rate cut.

The odds for such a move stands at 27%, dropping from about 50% at one point last week.

Meanwhile, Italy's Treasury started marketing a new 30-year BTP bond via a pool of banks.

The initial yield guidance for the issue, maturing on October 1, 2054, was set at around 15 basis points over the outstanding BTP due October 1, 2053, a lead manager said.

(Reporting by Sruthi Shankar in Bengaluru; Editing by Amanda Cooper and Gareth Jones)