June 5 (Reuters) - Euro zone government bond yields were on track for their first weekly increase since mid-May, as investors grew increasingly cautious about the prospects for a swift U.S.-Iran deal to reopen the Strait of Hormuz.

The Iran-backed Hezbollah militia rejected a new ceasefire in Lebanon on Thursday, undermining U.S. President Donald Trump's efforts to halt fighting there and forge a peace agreement to end the Iran war.

A reopening of the Strait of Hormuz could ease energy‑driven inflation pressures and reduce expectations of further central bank rate hikes, pushing bond yields lower.

Germany’s 2-year yields <DE2YT=RR>, more sensitive to expectations for policy rates, fell 0.5 basis points to 2.65% and were set for a 12-bp weekly increase. They reached 2.771% in late March, the highest since July 2024.

Money markets are pricing the ECB deposit rate at 2.65% by December EURESTECBM5X6=ICAP, which implies two rate hikes and a 60% chance of a third move. They also indicated a 90% chance of an initial rise this month and a second one in September.

Germany’s 10-year government bond yield <DE10YT=RR>, the euro area’s benchmark, was roughly unchanged at 3.02% and on track for a 9-bp weekly rise. It reached 3.13% in late March, its highest level since June 2011.

Investors are also awaiting the U.S. employment report later in the session, which could offer further clues about the Federal Reserve's policy path.

Italy’s 10-year government bond yields <IT10YT=RR> rose 1.5 bps to 3.83%, with the yield gap of Italian government bonds versus bunds <DE10IT10=RR> at 73 bps.