U.S. Treasury yields rose, joining their French and Spanish counterparts to start the week.

U.S. Treasury yields shook early softness and rose toward multidecade highs reached last week. The 10-year rose to 5.326% from Friday's settlement of 5.276% and the 30-year edging higher to 5.683% from 5.629%.

The two-year yield, which is more reactive to expectations of interest rate moves by the Federal Reserve, rose to 4.841% from 4.823%, while markets priced in an interest rate hold by the Federal Reserve this month.

Fresh indications of U.S. economic resilience helped keep yields rising. The Institute for Supply Management's purchasing managers index for services providers was 54.9 in September, compared with 55.4 in August. A reading above 50 suggests economic growth.

French yields moved on building concerns over the country's indebtedness, while Spanish government-bond yields increased after the government announced a snap election.

French 10-year government bond yields increased 231.8 basis points to 4.873% in Europe's midday trade, according to Tradeweb. They hit a peak of 4.993% Friday, their highest level since 2002 amid concerns that the government's recent budget proposal will struggle to be approved by a fragmented parliament. By contrast, 10-year German Bund yields were little changed at 3.457%.

The French-German 10-year bond spread stood at 140.44 basis points, having spiked Friday at a near 15-year high of 158.67 basis points.

"In European government bond spreads, we would not attempt to catch the falling knife yet, as an agreement on the French budget is a long way off and the European Central Bank is unlikely to act on spreads yet," Commerzbank rates strategist Hauke Siemssen said in a note.

Fiscal concerns should keep yields under sustained pressure, except for Bunds, he said.

Spanish 10-year yields increased 3.4 basis points to 4.119%, having hit 4.219% Friday, which was the highest since December 2013. Spreads between Spanish and German 10-year yields rose on the day to 66.10 basis points, albeit staying below a peak of 74.18 basis points reached Friday.

Spanish Prime Minister Pedro Sanchez called snap elections for next month following protests against high housing costs. Recent polls suggest the elections, set to take place on Nov. 29, could result in a right-wing coalition government between Spain's main conservative People's Party and the anti-immigration Vox party.

"Unrest in Spain and France underlines the difficult position governments are facing," Wealth Club chief investment strategist Susannah Streeter said in a note.