U.S. Treasury and European government bond yields turned lower Tuesday, reversing course, on optimism that diplomatic efforts could progress a reopening of the Strait of Hormuz.

Yields remain at elevated levels, though, due to continuously high oil prices, lingering concerns over budget deficits and supply pressure from both government and corporate bonds.

The 10-year U.S. Treasury yield fell 3.7 basis points to 4.926%, while the 10-year German Bund fell 1.5 basis points to 3.434%, according to Tradeweb. The 10-year French OAT yield remained an outlier in the eurozone, rising 1.8 basis points to 4.477%, causing the 10-year OAT-Bund spread to widen to 104 basis points. The 10-year U.K. gilt yield fell 2.4 basis points to 5.179%, while its previous increases came following higher-than-expected public sector borrowing in August.

Investors anticipate diplomatic progress in the U.S.-Iran conflict. U.S. President Trump told Fox News on Sunday that he is in "deciding mode" about next steps with Iran, and didn't rule out meeting his Iranian counterpart Masoud Pezeshkian who is expected in New York for the UN General Assembly this week. Investors also look forward to a meeting between Trump and Chinese President Xi Jinping later in the week.

Still, budget deficit issues continue to exert an upward pressure on bond yields, or at least prevent them from significant falls.

"Even if oil prices move lower, we do not think that long end rates could rally significantly," Mohit Kumar, global economist at Jefferies said in a note. "The deficit picture, particularly in Europe, is concerning as we head into the budget discussions in Q4 and elections next year," he said.

However, the 10-year French OAT-German Bund yield spread is expected to consolidate around 100 basis points as the market adjusts to this new reality, Chris Attfield, European rates strategist at HSBC, said in a note.

"There is little point in trying to draw 'lines in the sand' beyond which spreads will not rise, but 120 bps may be the next psychological level in any further spread weakness," he said. Eurozone yield spreads have been systematically widening in response to the surge in yields, but France's move is far larger than HSBC would expect given its debt-to-GDP ratio, he said.

Later in the day, investors will look at the U.S. Treasury's $69 billion auction of two-year Treasurys.

"Overall, while we are sensitive to the high level of outright yields, we ultimately think the macro backdrop will weigh on the supply process, and the auction will likely require more of a concession in order to be digested smoothly," J.P. Morgan rates strategists said.

Supply in Europe comes from Germany auctioning 5 billion euros ($5.73 billion) in October 2031-dated federal notes, or Bobl, and Italy syndicating a new October 2038-dated green BTP.