LONDON, July 3 (Reuters) - Euro zone bond yields dropped on Wednesday after survey-based data showed a sharp slowdown in the U.S. services sector in June, bolstering expectations for interest rate cuts from the Federal Reserve and other central banks this year.

Germany's 10-year bond yield, the euro area benchmark, was last down 6 basis points (bps) at 2.549%, dropping from around its highest in three weeks. Yields move inversely to prices.

The Institute for Supply Management's gauge of nonmanufacturing activity dropped to its lowest level since May 2020, with a measure of new orders tumbling. Separate data showed U.S. weekly jobless claims rose last week in a sign the Labour market is slowing.

The U.S. 10-year Treasury yield, which sets the tone for borrowing costs around the world, fell 9 bps to 4.343%.

Shorter-dated yields fell less far, a reflection of the fact that they have risen by less than longer yields - which have been driven by U.S. and European politics - in recent days.

Germany's 2-year bond yield, which is sensitive to expectations about European Central Bank (ECB) interest rates, was last down 1 bp at 2.899%.

Elsewhere, the risk premium investors demand to hold French debt narrowed on Wednesday as the prospect of National Rally (RN) securing a majority in France's parliament lessened, as anti-RN candidates coordinated a series of withdrawals in a bid to block the far right.

More than 200 candidates from the Left Alliance and President Emmanuel Macron's party confirmed they would step aside from Sunday's second-round election, as they called on voters to select whichever candidate was best placed to defeat the local RN rival.

"The strategy would significantly limit the chances of Le Pen winning an outright majority," Jefferies chief Europe economist Mohit Kumar said in a note, referring to RN leader Marine Le Pen.

"With both the far right or the far left unable to have the numbers to implement extreme policies, the scenario should be a near-term positive for the markets."

France's 10-year bond yield was last down 8 bps at 3.253%.

The gap between French and German 10-year sovereign bond yields - a gauge of the premium investors demand for the extra risk of holding French bonds – tightened to 67.8 bps, its narrowest since June 13. It was last at 71 bps.

The spread hit 85 bps on Friday, its widest since 2012, and despite falling back after the first round of the French election, it remains more than 20 bps wider than before Macron called the election on June 9. (Reporting by Harry Robertson and Samuel Indyk; Editing by David Holmes and Bernadette Baum)