U.S. Treasury yields declined on Monday, while eurozone government bond yields rose, pushing the 10-year Bund yield to a new 15-year high as fresh military escalation between the U.S. and Iran lifted oil prices.

The fall in U.S. Treasury yields reversed a sharp increase in short-dated yields on Friday after Federal Reserve Chairman Kevin Warsh made clear that returning inflation to the 2% target was his priority, suggesting that interest rates might need to rise.

The two-year Treasury yield, which rose 11.8 basis points on Friday, fell 2.5 basis points to 4.323%. The 10-year Treasury yield fell 1 basis point to 4.710%.

In the eurozone, yields rose after U.S. forces attacked two Iranian rocket launchers in the Strait of Hormuz on Sunday, according to the U.S. Central Command, risking a return to all-out conflict in the region. Oil prices rose above $90 per barrel on the news, last trading at $91.14, up 3.5% on the day.

"The exchange was limited, but it marks the first U.S. strike on Iran's forces in more than a month and highlights the risk of renewed escalation," Sofie Liv Petry, assistant analyst at Danske Bank said in a note.

The 10-year German Bund yield rose as high as 3.290% in opening trade, a level unseen since 2011, according to LSEG data.

Warsh said during a speech at the Jackson Hole symposium on Friday that he was impressed by the economy's performance but expressed concern about inflation remaining above target. Thus he left the door open to raising interest rates in the coming months.

Investors significantly stepped up expectations for a rate hike in September following the speech. U.S. money markets on Monday priced a 60% probability of a rate increase at the next meeting on Sept. 16, compared to 35% Friday before Warsh spoke, according to LSEG.

"While Warsh did not send clear signals on the timing of rate changes, the speech was supportive of market expectations of a rate hike during the fall--whether in September or by year-end," said Elisabet Kopelman, U.S. economist and Fed watcher at SEB, in a note.

At the same time, investors were relieved at the clarity Warsh offered on the outlook after he had left investors uncertain about the Fed's policy path and its commitment to tackling inflation following the central bank's meeting in July.

Warsh was "walking back his communication mistakes in July," Kopelman said.

Larry Holzenthaler, senior portfolio manager at Catalyst Funds, said Warsh "was successful in re-establishing confidence."

"He came across as very focused on inflation and bringing it back in line with the Fed's 2% target."

On Friday, the market seemed to react exactly as the Fed would want, with short-term rates higher and long-term rates marginally lower following Warsh's comments, Holzenthaler said.

"Investors should clearly expect that the Fed is going to raise rates if it needs to," he said.

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