LONDON, July 9 (Reuters) - Euro zone government bond yields edged up on Tuesday, staying higher after Federal Reserve Chair Jerome Powell said inflation "remains above" its 2% target but has been improving.

Speaking to the U.S. Senate Banking Committee, Powell said "more good data would strengthen" the case for central bank interest rate cuts.

Germany's 10-year bond yield, the benchmark for the euro zone bloc, was last up 4 basis points (bps) at around 2.56%, compared with 2.53% just before Powell started speaking.

U.S. Treasury yields rose, dragging their European counterparts with them.

"Powell's comments are not too much of a surprise as of now but his Q&A (question and answer) session could be interesting," said Commerzbank rates strategist Rainer Guntermann.

"He is slightly more optimistic on inflation."

Most euro zone bond yields have fallen over the last week as data have suggested the U.S. economy is slowing, adding to hopes that the Fed can cut rates this year and bolstering expectations of further reductions from the European Central Bank.

Money markets price in a roughly 76% chance of a quarter point cut in September, broadly unchanged from before Powell started speaking.

The ECB meets next week and is expected to keep policy steady, having cut rates in June.

In Europe, focus remained on France following Sunday's second-round parliamentary election which resulted in a hung parliament.

Leaders from the left-wing bloc that came first in France's legislative election and the runner-up centrists have engaged in a frenzied race to be first to cobble together a viable government, lawmakers and other sources told Reuters on Tuesday.

France's 10-year bond yield was up 8 bps in late trade at 3.25%. The closely watched gap between French and German borrowing costs was wider at around 67 bps but down from the highest since 2012 in late June at 85 bps on fears of a far-right victory.

"Whereas in the U.S. we see the rate-cutting narrative picking up momentum, in the euro zone the direction is less evident," Michiel Tukker, senior European rates strategist at ING, said.

"The data in the euro zone has simply been more mixed regarding the direction of the economy, with headline inflation coming down, services inflation and wage growth remaining stubborn, and labor markets showing few signs of deterioration."

Italy's 10-year yield rose 7 bps to 3.96% after falling for the previous two sessions, and the gap between Italian and German yields was around 4 bps wider at 140 bps.

Germany's two-year bond yield, which is more sensitive to ECB rate expectations, was up 2 bps at around 2.93%. (Reporting by Harry Robertson and Dhara Ranasinghe; Editing by Andrew Heavens, Emelia Sithole-Matarise and Josie Kao)