Updated for European close

By Alun John

LONDON, June 12 (Reuters) - Euro zone bond yields fell on Friday, catching up with overnight remarks from President Donald Trump that a deal between Iran and the U.S. could be signed as soon as this weekend and reopen the key Strait of Hormuz.

Shorter-dated, central bank-sensitive bonds led the rally, with Germany's two-year yield down 5 basis points at 2.619%, earlier touching its lowest in 10 days at 2.581%. Italy's two-year yield fell 6 bps to 2.804%. DE2YT=RR, IT2YT=RR

Trump said on Thursday he was calling off new strikes on Iran because a deal was now ready, with optimism building further on Friday. A Western source told Reuters a memorandum between Washington and Tehran to end their conflict could be signed as soon as Sunday.

Trump later called reports of the terms in the proposed memorandum to end the war inaccurate, but investors clung to hopes that a deal could be close.

The 10-year German yield, the euro zone benchmark, dropped 2 bps to 3.002%. DE10YT=RR

Yields have been moving in step with war headlines, as traders weigh how long the Strait of Hormuz might remain closed. Prolonged disruption and elevated oil prices risk feeding through into broader inflation and forcing central banks to raise interest rates.

Underscoring this risk, the European Central Bank raised rates on Thursday, aiming to curb inflation before higher fuel costs spread through the economy.

ECB President Christine Lagarde offered few clues on future policy at her post-decision press conference, reiterating the bank's "data-dependent" and "meeting-by-meeting" approach.

Money markets currently price roughly a 30% chance of an ECB rate hike in July, with a move by September seen as almost certain.

"Taking the guidance at face value, this means that July is 'live'. However, we do not think that it is the most likely," BNP Paribas analysts said in a note.

They pointed to Lagarde's comment that the ECB is not seeing second-round effects on wages. "We view a July move, therefore as more 'shock dependent' than 'data dependent' ... for example, a material increase in energy prices – that changes the scenario within which the ECB operates and could prompt a move."

Two sources told Reuters that policymakers see holding rates steady in July as the most likely outcome, if energy prices stay near their current level.

However, public remarks from several ECB policymakers on Friday kept the possibility of a July move on the table.