U.S. Treasury yields rose, joining their French and Spanish counterparts as the global bonds selloff shows no signs of ending.

U.S. Treasury yields shook early softness and rose toward multidecade highs reached last week. The 10-year rose to 5.310% from Friday's settlement of 5.276% and the 30-year edged higher to 5.664% from 5.629%.

The two-year yield, which is more reactive to expectations of interest rate moves by the Federal Reserve, rose to 4.831% 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.

Citi analysts observed in a note that "a rising number of industries increasing employment levels continues to imply low unemployment," while comments in the ISM survey responses "noted some drag on activity from higher rates, although most comments continue to indicate issues stemming from higher input costs."

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 rose as high as 4.925%, before settling at 4.865%, little changed from Friday and near a 24-year high reached last week, as investors worried that the government's recent budget proposal will struggle to be approved by a fragmented parliament.

The 10-year German Bund yields settled at 3.492%, keeping the spread between French and German yields relatively wide due to the fiscal concerns in France.

"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 settled at 4.136%, after hitting 4.219% Friday, which was the highest since December 2013.

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.