Euro zone bond yields dipped on Tuesday as oil prices hovered around four-month lows and investors waited for news on possible talks between in Qatar this week as well as inflation data.

Germany's 10-year bond yield (DE10YT=RR) fell 1.5 basis points to 2.89%, to trade just above its lowest in four months. Yields move inversely to prices.

Germany's 2-year bond yield (DE2YT=RR), which is sensitive to European Central Bank rate expectations, fell 2 bps to 2.512%.

The U.S.-Iran peace deal has come under threat as both sides traded attacks, but the White House said it is sending envoys to Doha this week for further talks on the agreement.

Brent crude oil ICEEUR:BRN1!, the global benchmark, was slightly lower at $72.90 on Tuesday. It has fallen to around its lowest levels since the war started in late February as oil has begun to flow again through the Strait of Hormuz.

Bond traders were also watching euro zone June inflation data, with figures from France showing prices rose less than expected in June, at a 2% rate.

Data for four Germany states showed inflation cooled in May, nudging bond yields lower. Figures for the euro zone bloc are due on Wednesday.

But at the ECB's annual conference in Sintra, Portugal, policymakers said the oil price shock would continue to affect the economy and they remained concerned about inflation.

"Keeping a somewhat hawkish bias makes sense," said Michiel Tukker, rates strategist at ING.

"Only later this year will we have a better understanding of the second-round inflation impact and more certainty about the trajectory of oil."

Money markets are pricing in one more 25 bp rate hike from the ECB this year, after it raised rates earlier this month.