May 17 (Reuters) - Euro zone sovereign bond yields rose on Friday after European Central Bank (ECB) board member Isabel Schnabel said the central bank should be cautious about rate cuts beyond June.

Still, yields are on track for a weekly fall as U.S. data this week showed inflation and the economy had cooled in April, supporting expectations for Federal Reserve rate cuts.

"Depending on the incoming data and our new Eurosystem staff projections, a rate cut in June may be appropriate," Schnabel said in an interview with Nikkei in Frankfurt that was posted on its website on Friday.

"But the path beyond June is much more uncertain. Recent data have confirmed that the last mile of disinflation is the most difficult," she said.

Germany’s 10-year yields, the euro area's benchmark, rose 3 basis points (bps) to 2.47% and were set to end the week down 5 bps.

Markets were pricing in 68 basis points (bps) of ECB rate cuts in 2024, down from 72 on Thursday, and 46 bps for the Fed from 50 bps.

Italy's 10-year yield rose 3 bps to 3.78%, and the gap between Italian and German 10-year yields -- a gauge of the risk premium investors seek to hold bonds of the euro area's most indebted countries -- was flat at 130 bps.

Germany's 2-year yield, more sensitive to policy rate expectations, was up 1.5 bps at 2.93%.

The spread between U.S. 10-year Treasuries and German bunds -- a gauge of the expected policy path divergence between the ECB and the Fed -- tightened 2 bps to 190 bps. (Reporting by Stefano Rebaudo, editing by Neil Fullick)