Italy's anti-establishment parties formed a coalition government on Friday to end three months of deadlock.
Italian bond yields fell after soaring last week on fears a snap election would be called that might effectively become a referendum on euro membership.
The spread on Spanish bond yields over benchmark German Bunds also narrowed after a new prime minister was sworn in in Madrid, though Socialist Pedro Sanchez's minority administration faces a tough baptism from a revived independence drive in Catalonia.
At the same time, U.S. Treasury yields rose, with the 10-year yield hitting one-week highs, as investors pared safe-haven holdings of lower-risk government debt amid reduced anxiety about the political turmoil in Italy and Spain.
Benchmark 10-year notes last fell 14/32 in price to yield 2.9442 percent compared with 2.895 percent late on Friday.
The dollar index fell 0.18 percent to 94.04, with the euro up 0.04 percent to $1.1703.
U.S. stocks rose, led by gains in technology shares. Strategists said Friday's robust jobs data gave investors heightened confidence that the U.S. economy remained strong. The Nasdaq hit a record closing high, while the S&P technology index was up 0.8 percent.
"It's kind of a reset from last week. The European situation improved. We saw our rates in the 10-year move up a little bit, which may be indicative of growth here in the U.S. relative to the rest of the world," said Bucky Hellwig, senior vice president at BB&T Wealth Management in Birmingham, Alabama.
"We had some follow-through from some of the data that was out on Friday. As you drill down on that employment report ... it shows not only a strong economy but an economy that's broadening out. There's this idea that U.S. growth is picking up and pulling away from the pack, so that was bullish for stocks today."
The Dow Jones Industrial Average rose 178.48 points, or 0.72 percent, to 24,813.69, the S&P 500 gained 12.25 points, or 0.45 percent, to 2,746.87 and the Nasdaq Composite added 52.13 points, or 0.69 percent, to 7,606.46.
MSCI's gauge of stocks across the globe gained 0.7 percent. European shares rose 0.2 percent.
While the risk of political crisis receded in Europe, concerns over a possible global trade war rumbled on in the background.
Finance ministers of the closest U.S. allies vented their anger on Saturday over Washington's imposition of metal import tariffs, setting the tone for a heated G7 summit in Quebec.
Canadian Prime Minister Justin Trudeau this week plays host to a summit of the Group of Seven leading industrialized nations with six of the seven members outraged at the United States over a slew of recent moves by President Trump.
Trudeau, who wants the June 8-9 meeting to focus on economic growth, insists he can handle the challenge, though insiders and analysts say he will have to fight to keep the grouping together at a time when Trump's trade and diplomatic moves have isolated the United States and risk undermining the G7's relevance.
Washington also remained at odds with Beijing. China warned the United States on Sunday that any bilateral agreements reached on trade and business would be void if Washington implemented tariffs and other trade measures.
Oil prices slid, pressured by growing U.S. production, possible global supply growth and nagging trade tensions.
Benchmark Brent crude oil lost $1.50 to settle at $75.29 a barrel, while U.S. light crude fell $1.06 to settle at $64.75.
(Additional reporting Richard Leong in New York; Editing by Chizu Nomiyama and James Dalgleish)
By Caroline Valetkevitch
