U.S. Treasury and European government bond yields hovered around multiyear highs as investors remained concerned about long-term uncertainty .

The 30-year Treasury yield touched 5.587%, its highest intraday level since May 2004. The 10-year traded at 5.265%, on pace to settle at a 19-year high for the eighth time this month.

Yields have been rising on stronger-than-expected economic indicators released earlier this month, but on Tuesday the upward pressure remained despite lukewarm data. July home prices rose less than inflation, falling in real terms, for the 14th consecutive month, while August job openings were less than expected.

Consumer confidence surprisingly declined in September, with a growing number of respondents in the Conference Board survey anticipating higher interest rates over the next 12 months.

Oil prices slipped but remain elevated, amid lingering Middle East tensions, supporting inflation worries.

Front-month Brent for November fell 1% at $104 a barrel.

With yields at such high levels, some market participants consider that the bond selloff has potentially gone too far.

High yields "could attract investors as fixed income becomes increasingly competitive with equities as a source of capital for the insatiable appetite of AI demand," said Richard Hunter, head of markets at Interactive Investor.

J.P. Morgan strategists described 30-year Treasurys as "oversold," though they are wary that the trend for higher yields could continue.

"We are now left waiting for renewed evidence that would suggest the market is starting to respond to those conditions after we were stopped out of our long trade last week," they said in a note.

In Europe, the bond selloff took a breather and the 10-year German Bund yield fell 4.5 basis points to a still high 3.601%.

Strong economic data, a resilient labor market, robust AI expenditure, easier fiscal policy, and persistent energy inflation are forcing markets to reconsider the level at which rates could find an equilibrium, said Mauro Valle, head of fixed income at Generali Asset Management, in a note.

"If the U.S. and Iran start to negotiate again, the 5% level could be a neutral one for the next few weeks," he said.

Yields remain under upward pressure from energy prices "as the U.S. and Iran appear to be stuck in their negotiations," Antti Ilvonen, senior fixed income and FX analyst at Danske Bank, said in a note.

High oil prices are fueling market expectations of further interest-rate hikes by the Federal Reserve following the one earlier in September. Money markets currently price in 100 basis points of Fed rate hikes over a 12-month horizon, according to LSEG.

Analysts said high yields also reflect the strength of the U.S. economy.

"The surge in the 10-year Treasury yield to approximately 5.25% reflects higher oil prices and a strong U.S. economy more than AI debt issuance or fiscal concerns," said James Reilly, senior markets economist at Capital Economics.

Eurozone bond yields cannot take much comfort either from flash estimate data showing Spanish annual inflation at a three-and-a-half-year high of 5.0% in September, up from 4.6% in August.

Investors will likely assess U.S. data this week for clues on the trajectory of interest rates.

ADP's private payrolls report is due Wednesday, followed by weekly jobless claims figures Thursday and the key nonfarm payrolls report Friday. The PCE prices data, the Fed's preferred inflation measure, are also due Wednesday.

Markets are also likely to react to a full slate of Fed officials' speeches, which have been hawkish of late.

Jessica Coacci contributed to this article.